Nancy's mother's drinking problem holds another layer besides straightforward self-medication when you realize that alcohol actually prohibits REM sleep.
Tina mentions that nightmares sometimes foreshadow earthquakes; exactly what signifies Freddy's presence in Wes Craven's New Nightmare years later.
Nancy is rightly outraged when she realizes that her father used her as bait to draw out and arrest Rod...but it could easily be this incident that gives her the idea to pull the exact same trick on Freddy in the climax.
Given the way Freddy died, his entire body should be horribly burned. However, in Nancy's dream in the school, when Freddy pulls his sweater up and cuts his chest, his torso only has very minor scarring on one side, and he even has chest hair. Also, the palm of his right hand is clearly shown several times through the hole in the glove and there's no scarring at all.
Its possible that the form Freddy takes isnt exactly how he looked, but an approximation of how his burn scars looked. In his defense, if he tried to look like how he really looked when he died, there wouldnt be much of Freddy to see.