Assuming it's Doug, no one checks the rooftop (only on occasion), and he was still wasted AND couldn't move due to the sunburn.
No-one would have heard him. He's high above the street, and the hotel windows are all sealed for the aircon.
Considering where they found Doug, it's almost impossible he didn't die of dehydration. He went out the night before drinking to capacity, then spent the next 36 hours with no water, rain, or shade.
He did have a sheet....
It's not impossible to survive, but he was damned lucky.
The roof wasn't flat. He did have some shade, though only from objects about 2-3 feet high.
Mike Tyson's tiger is only bothered by the protagonists when they're sober.
That one's an old trick. The animal senses your fear, etc, etc. Whether it's true or not, someone else will have to answer.
Here's two possibilities. One is that the guys' tension while sober triggered the tiger's aggression, since in the wild a tense animal is either potential prey or a potential attacker. The other is that, while the tiger was comfortable on his home turf as the guys led it into the car, he became increasingly anxious after being away from his territory for a while (felines become strongly attached to familiar surroundings and can take a while getting used to a strange place). It's probably some combination of the two, actually.
Nobody moves in to stop Alan from cutting his palm open?
Considering the circumstances, they're all standing around, drinking, laughing, and then suddenly someone whips out a knife and cuts himself with it? It's not unreasonable to suppose they'd all be standing there in shock for the second it would take him to complete the act.
Why did Mike Tyson not have a tranquilizer gun? WHO KEEPS A PET TIGER WITHOUT A TRANQ GUN?!?
If anyone could manage a tiger without a tranq gun, it would be Mike Tyson.
Would you really build a hotel with a roof door that locks automatically, and no other way to get down? What if someone's on the roof when there's a fire?
Patrons of the hotel are not supposed to be on the roof. It's probably presumed that people who are on the roof for legitimate reasons will have/be given a key to keep it unlocked.
Actually The real headscratcher is why is the door locked from the outside? Roof door locks are reversed. The inside is locked while the outside is unlocked. In case someone drops/doesn't have the keys so they won't be trapped. Then again they might have jammed the lock.
Why was Doug hanging out with his friends, looking at pictures, for a big part of his wedding night? Shouldn't he be, you know, with his wife? Or at least mingling with the other guests?
Guess he had some free time after everything else was done?
At the vast majority of weddings, it's about the bride. No-one is going to begrudge the groom from wandering off with his best friends for a half-hour, especially towards the end of the night.
I know it might be part of Don't explain the joke, but when Alan says he can't lose any more people, listing off his grandfather, why does everyone skip over the fact that said grandfather died in WWII, thus long before Alan was born, which means Alan would never have met him? Even Phil doesn't seem to be fazed.
It is the first hint that Alan is more than human...
He will have had more than one Grandfather...
Because at that point they know how Alan is and that it's not worth pointing that sort of thing out to him.
Admittedly the movie wouldn't work without this, but it's still a big problem - Doug is stranded on the roof after the guys go up there to start the party, but especially in Las Vegas, a hotel roof is completely inaccessible by guests, to prevent people from committing suicide after a big losing streak. In fact, the doors work the opposite way - locked from inside the building, but easily opened from outside - in order to specifically prevent the kind of situation that happens in the movie.
The point is that they got so drunk that they managed to do things that should be effectively impossible for them to do. Anyone that's worked computer tech support will tell you that people frequently manage to do those sorts of things even without the aid of alcohol. And a brief glance at some rather amazing car crash photos will show you that people under the affects of alcohol will find ways to violate a layman's understanding of physics.
In the second movie, during the "Allentown" song Stu was singing in the boat, where did they get the guitar?
Why is Alan always forgiven despite directly responsible for all the events in the movies and generally is shown as a dangerous sociopath yet treated like an innocent manchild?
He's really not. He's given some leeway by some of the guys because they understand that he's not really mentally all there, so they basically do treat him like a child and assume he's not entirely responsible for his own behavior. Stu doesn't really forgive him, as shown by the sequel, but at the end of the movie he's accepted that Alan probably did him a favor by opening his eyes to what crap his life had become, so he's nice to him for a little while.
How did Chow know precisely where the half of the gold he couldn't steal was hidden right inside Marshall's basement? And also, how did Chow even know exactly the master plan to breaking into Marshall's house?
Part III's ending. I get that staying away from Chow is a good thing, but how was association with Chow basically the cause of all of Alan's actions? I mean, the plot of Part III is Phil, Stu, and Doug taking Alan to rehab because of the way he has been behaving, until Marshall and his men abducted them and only targeted them because of their association with Chow.
We only see Alan with no knowledge of Chow in the first film, and he becomes increasingly weirder as the series unfolds; maybe Chow's the reason Alan becomes so extremely weird nobody can put up with him.
Talking of Part III's ending... drunk tattoos are one thing, but where did Stu find a doctor willing to give him breast implants in under a day while completely wasted?