Has anyone else ever tried to keep track of all the plaid cases?

Where is the fun when there is so much else of the film to enjoy.

Its that man again!!

That is fun. It's possible for the most part. A person needs to keep track of who is in which room and then also which bag is in which room.

The timeline of the bags does work out (but with a few continuity problems).
The 4 bags are labeled as: Mr. Smith's (the government spy) (Bag #1/Files), Howard's (Bag #2/Rocks), Judy's (Bag #3/Clothes), and Mrs. Van Hoskins (Bag #4/Jewels).
Since the men in suits are rarely called by their characters' names (other than Fritz), I used nicknames: Mr. Smith ("Spy"), Mr. Jones ("Golf Guy"), Harry ("Jewel Thief").
The rooms are labeled as: number/occupant.

Here is the summary:
- Howard & Eunice check into the hotel, and Eunice takes Bag #2/Rocks to her room (Room 1714/Eunice).
- "Golf Guy" looks under the door of Mrs Van Hoskins' room (Room 1715/Mrs VH), sees a plaid bag, and assumes it is Bag #1/Files but really it is Bag #4/Jewels. "Golf Guy" then enters Room 1717 because it is already open.
- Judy enters Howard's room (Room 1716/Howard) with Bag #3/Clothes & sews up Howard's torn jacket.
- "Jewel Thief" looks under the door of Mrs VH's room (Room 1715/Mrs VH), sees the plaid bag, and then enters Room 1711 (his room).
- "Golf Guy" enters Room 1715/Mrs VH through the adjoining door, steals Bag #4/Jewels (assuming it is Bag #1/Files), returns to his room (Room 1717), and calls his chief.
- "Spy" enters Room 1715/Mrs VH through the other adjoining door (connecting to his Room 1713), places Bag #1/Files on the closet top shelf, covers it with a pillow, and returns to his own room.
-"Jewel Thief" enters Room 1715/Mrs VH, steals Bag #1/Files (assuming it is Bag #4/Jewels), leaves Room 1715/Mrs VH, hears the elevator bell, and enters Room 1714/Eunice. (His accomplice, Fritz, must have given him a master key.) "Jewel Thief" slides Bag #1/Files under Eunice's bed (not knowing Bag #2/Rocks is next to it under the bed) and later tells Fritz where he put the bag. Since "Jewel Thief" didn't get the stolen bag out of the hotel, Fritz says he will return the bag to Mrs VH's room.
- Fritz tells Eunice a pet snake escaped and she goes into the bathroom. Fritz takes Bag #2/Rocks (not knowing Bag #1/Files is still under the bed), leaves Room 1714/Eunice, enters Room 1715/Mrs VH, and places Bag #2/Rocks onto her bed. Fritz later tells "Jewel Thief" to enter Room 1715/Mrs VH through the Room 1717-adjoining door, get the bag, and bring it to the basement.
- Eunice slides Bag #1/Files out from under her bed, exits her room, & places it in front of Room 1716/Howard.
- Howard picks up Bag #1/Files, gets his jacket from the door's laundry reservoir, enters his room, & puts Bag # 1/Files into his closet. Howard finds Judy taking a bubble bath with Bag #3/Clothes next to the tub. [Notice Howard's RED PLAID bow-tie and cummerbund.]
- "Golf Guy" overhears "Jewel Thief" tell Eunice that he has to go to Room 1717/Golf Guy, so "Golf Guy" escapes onto the exterior window ledge carrying Bag #4/Jewels & his golf bag.
- "Jewel Thief" enters Room 1717/Golf Guy, then enters Room 1715/Mrs VH through the adjoining door, steals Bag #2/Rocks, crawls on the floor (with Mrs VH sleeping in her bed), exit Room 1717, returns to his room (Room 1711).
- Eunice hears a ruckus coming from Howard's room, bangs on the door (Judy goes out the window), enters Howard's room, and finds Bag #3/Clothes in the bathroom. Howard takes Bag #3/Clothes & brings it into the bedroom.
- "Spy" enters Room 1715/Mrs VH, realizes his bag is missing from the top closet shelf, leaves Room 1715, crosses the hall into Room 1714/Eunice. During the fire escapade, he opens the adjoining door (from Room 1714/Eunice to Room 1716/Howard), steals Bag #3/Clothes, & returns to his own room.
- "Golf Guy" sidles along the exterior window ledge (where Judy is dangling), breaks through the glass, & falls into Room 1716/Howard (with Bag #4/Jewels & his golf bag). [There are continuity problems with Bag #4/Jewels in this scene. "Golf Guy" falls on top of Bag #4/Jewels with curtain over his face. There is a quick cut to Judy, and then back to the room where "Golf Guy" is still covered by the curtain but Bag #4/Jewels has magically moved to the front of the bed (sitting upright between the bed & room service table). Fritz & "Jewel Thief" enter the room, remove the tablecloth to smother the fire, and Bag #4/Jewels has disappeared again (not to be seen again until the morning.]
- The next morning, "Golf Guy" sits out front of the hotel without a plaid bag. His golf bag still has a smoking club cover from the fire. [Also notice the RED PLAID carpet outside the hotel next to him.]
- "Jewel Thief" brings Bag #2/Rocks to the basement (as instructed by Fritz).
- "Spy" sits in his room & smokes a cigarette with Bag #3/Clothes on the table next to him.
- Howard sleeps in his room with a red plaid bag next to him. At this point, it could be Bag #4/Jewels (left by "Golf Guy" who we know is now bagless) or Bag #1/Files (retrieved from his closet). [It is never shown how Bag #1/Files leaves the closet.]
- "Spy" overhears Howard & Eunice arguing, opens his door, sees Howard's red plaid bag, & realizes there are two red plaid bags. He opens Bag #3/Clothes & realizes he has the wrong bag.
- "Jewel Thief" holds Bag #2/Rocks (covered in a sheet), Fritz tells him to take it to 459 De Rello St on the 2nd floor, which is overhead by Judy.
- Judy & Howard meet up in the lobby each carrying a plaid bag (either could be Bag #1/Files or Bag #4/Jewels). They separate. Judy calls Eunice to give her the wrong address (459 De Rello St, 2nd floor), steps onto the down escalator, & places the plaid bag on the railing. Fritz (standing next to the escalator) sees that there are now 2 red plaid bags.
- "Spy" runs through the lobby, apparently sees Judy on the escalator with another plaid bag, bumps into Fritz, and gets on the escalator. Fritz & Spy now know there are at least 3 red plaid bags.
-Howard & Judy (with Bag #1/Files & Bag #4/Jewels) get into a blue taxi. "Spy" rushes out of hotel (with Bag #3/Clothes) and gets into a yellow taxi to follow Howard & Judy. "Golf Guy" emerges from behind a potted plant (the one he was sitting on earlier) and hails a taxi (presumably to follow "Spy" following Howard/Judy.
- Eunice arrives at the De Rello address & finds "Jewel Thief"& "Criminals" with Bag #2/Rocks.
-Howard & Judy enter the party as the following 2 yellow taxis pull up to the curb.
- Howard is asked to give a recital on his rocks. He opens his case, & it is revealed that he has Bag #4/Jewels. Judy gives him her case, and she has Bag #1/Files. [To me, it would have made more sense Howard to have Bag #1/Files because his bag should have been in his closet that morning. He brought Judy's bag into the bedroom (which was stolen by "Spy"), and "Golf Guy" left Bag #4/Jewels in the bedroom. It would be more logical if Judy took Bag #4/Jewels.]
- "Spy" enters the party with a gun and demands one of the bags. Howard slides Bag #1/Files over to "Spy", but he doesn't get a chance to open it.
- "Golf Guy" emerges from the balcony with a gun and demands one of the bags. "Spy" throws up Bag #3/Clothes, since he knows that he doesn't want that one. "Golf Guy" also doesn't get a chance to open the bag.
-"Jewel Thief" & "Criminals" enter with Eunice, who announces they have Bag #2/Rocks. One of the Criminals demands "Golf Guy" throw down Bag #3/Clothes & his gun. The Criminal then kicks away Bag #2/Rocks. Criminal doesn't get a chance to open the bag because "Golf Guy" jumps down and starts a brawl. [There is a continuity problem during the brawl. Before "Golf Guy" jumps down, we see two bags over by "Spy" (Bag #1/Files & Bag #2/Rocks). Howard kneels down, fumbles with Bag #4/Jewels (while Judy is swatting a "Criminal" with a floppy metal statue), and then Howard away towards the leather couch empty-handed. There is a cut to Hugh's pie-in-the-face gag. Then Bag #4/Jewels magically appears on the floor next to the black leather sofa, and Howard picks it up and places it on the couch seat. Howard & Judy jump on the couch for a charming moment with the swinging lamp, and then get off the couch to retrieve the other bags.]
- Howard holds Bag #4/Jewels (standing next to Bag #1/Files & Bag #2/Rocks) while Judy retrieves Bag #3/Clothes, and they leave for the big chase scene.

The "bag gag" is an amazing piece of writing! It takes several viewings to keep the bags straight. Once Judy and Howard scoop up all the bags at the party, it's pretty much pointless to try to track them after that point.