My thoughts on why this is overlooked.
I'm a huge Bond fan. I have VHS and DVD copies of most of the Bond Films, and watch them fairly regularly. I feel that The Living Daylights is one of the most underrated Bond films out there. Sure, it absolutely doesn't hold a candle to Goldfinger, The Spy Who Loved Me, or even Goldeneye, but I feel it still holds up well over time. I feel that the general negativity towards this film has more to do with the subject matter than the film making itself.
We all see Bond marathons on t.v., they're everywhere. People cant get enough of our beloved suave secret agent. Unfortunately, I almost never see TLD in these marathons, and I think that has to do with the connection to al-Qaeda through the Mujahideen. Here in the US, we are scared of terrorism, as evidenced by the tirade of freedoms we willingly gave up in order to combat it. For those who don't know the historical connections here, let me inform you. Back in the 80's, the Afghani resistance group known as the Mujahideen fought a war with the Russians, and the US (inspired by our fear of communism) supported the Mujahideen in the war. After the war, a group (led by Bin Laden) splintered away and became the terrorist group al-Qaeda.
So I believe the reason TLD doesn't get the airtime other Bond movies get is a purely political one, and to overlook it for those reasons would be giving into terrorism, because they win if we're afraid of them. I have always been a fan of the scene where they're sledding in the cello case, finishing with the line "we've nothing to declare!" as they pass the boarder. I'm also a fan of the occasional recasting of actors, like Joe Don Baker playing Whittaker in TLD, then playing Jack Wade in the Brosnan films, or Charles Gray playing the contact in Japan in You Only Live Twice, and Blofeld in Diamonds are Forever.
Stop trying to poke holes in the plot and enjoy the ride.