The play (all spoilers)

Some gems and some flaws.

First...Jim..inventor, time traveler, gullible idiot, peeper.
Howard...rival, devious, impulsive.
Please note that every paradox has two distinct possibilities depending on one's perspective and view of time travel.

So, Jim throws himself in the box and he's gone.
(A lot like Back to the Future)
Howard waits until Jim returns and shoots him dead.
This is actually Jim #3 but only if Howard can convince Jim to get back in the box twice.
Jim #1 arrives and sees Jim #3 dead.
Jim reenters the box despite being the absolute worst thing he could do.
Jim #2 arrives before Jim #1 but enters the front door, probably because he saw that Jim #3 entered through the garage.
Jim #2 enters and shoots Jim #3. The writers feel that this is due to the suggestion that Jim would shoot himself, a self-fulfilling prophecy. However, Jim only had to say freeze. There was no need to fire. His stated goal was to prevent his death from happening. So, he is so nervous about dying that he shoots himself.
Jim renters the box, becoming Jim #3 who will enter the house second after Jim#2 and is shot. This is poorly written. Jim #2 knows he will be shot, knows not to enter through the garage, and knows his former self has the gun and will shoot.
Why not just sit outside and wait 10 minutes? Why didn't he take the gun with him through time? Basically, by quick editing, the average viewer will get confused and not care too much about the plot.
There's still a Primer twist. Howard has also used the box to tell himself he must repeat his action of watching Jim leave for the first time.
This is a Primer reference, but without any value.
If Howard already made the mistake and Jim never time traveled again, then he wouldn't be lying dead on the floor.
And if Howard knows not to leave the house, he wouldn't need to time travel.
I guess they just wanted to play another paradox card.
So, Howard leaves and ruins the murder of Jim because Jim #1 comes back (amazingly last) and finds Howard stealing the flux capacitor and thus never goes back into the box.
Somehow, this means that Howard can replace the flux capacitor, get in the box and travel back, return to the house and tell himself not to leave before Jim returns and is tricked into re-entering the box. I guess we are suppose to believe that Jim returns, sees Howard leaving with the flux capacitor, sees dead Jim, and still believes when Howard says, "You shot yourself and now that your back, you need to send me (Howard) back so I can stop you from shooting yourself." Jim happily complies.
Next, Howard #1 even replaces himself to tell Jim #1 what happened. This means that previously, he did not accomplish this step correctly, although we saw that he did, so another paradox or a useless time travel just to create a scene of Howard talking to Howard #1.
Still, one more paradox...Howard already has a suitcase to steal the flux capacitor with foam padding cut out to the exact shape.
Did he use it a week from now and go back to before this incident? The only reason to do so would be to better protect the flux capacitor after stealing it. But, if he damaged it after stealing it, then how could he travel back in the first place. Either he can not travel back or there is no need to travel back.

One brief note..(purely for those who use geek-speak)..traveling back five minutes would place you almost 3 miles away from your first destination. Every Jim and Howard and Molly would have to arrive at the exact same location. So Jim #3 would not land two homes away while Jim #1 lands five blocks away. Also, traveling 24 hours would be logistically safer than five minutes where he could reappear inside a brick wall or in the middle of a highway. but who cares, its pseudo-Hollywood, right?