The big plothole make no sense
OK, to be fair, I am not completely sure if it constitutes a plot hole or not. But it certainly is a big goof or error that just doesn't make sense.
How does David end up in trouble? Let's look at the chain of events.
1) He sees a "Protovision" ad in a magazine, and wants to play those games before they reach the market.
2) He starts 'Wardialing' the whole area (code) where the corporation is located, planning to go through all the numbers until he gets to 'Protovision modem' that would not only be always turned on, connected to some meaningful computer that's also always on, not busy - AND - set to answer any random incoming modem call. (For all he knows, the corporation might not even HAVE a modem, considering the year)
3) Instead of using his research skills, efforts, energy and focus on simply trying to find Protovision's official phone and modem numbers (surely LESS effort than his research in this movie), he trusts some random number (that he does not verify to belong to Protovision, or research/check whom it belongs to, or anything) to be the Protovision modem number, and becomes obsessed in ..
4) ..trying to acquire the password to that system (though usually, systems, ever since early BBS's (had to use an apostrophe here), had 'login and password' - hard to imagine a MILITARY system not have one), so he begins his..
5) ..intense and intensive research on Stephen Falken.
See the plot hole yet?
I mean, he's researching this guy OBSESSIVELY, like a maniac, for weeks or so, even forgetting to go to school or contact his girlfriend (or whatever Sheedy's role really is here).
At some point, he should basically know pretty much _EVERYTHING_ about Falken. Everything - including the fact that a) he does NOT and NEVER did work for Protovision and b) he HAS and DID work for the U.S. Government, military, and so on and so forth.
Now, HOW can David still think it's Protovision's number, and the whole thing is not military? Why would David give up his Protovision computer games obsession so easily in favor of some slow, crappy, monochrome, ASCII-based door game? (If you don't know what a 'door game' is, research 'BBS games' or watch the old 'BBS documentary)
I mean, door games are fine, but real computer games have not only sound and music, but also multiple colors, proper sprites, animations, movement, realtime control and so on. The first proper 'multimedia'.
(Obviously, the quality of those things varied back in the day, but Atari 8-bit line and Commodore 64 were out in 1983)
Someone like David would NOT be this excited about a pretty crude, rudimentary, text-based 'war game', when he could play PROPER computer games after downloading them from Protovision (a hare-brained idea anyway, considering he might only find unfinished versions of the game that aren't as good as the final versions and so on).
He should know after researching Falken, that he's NOT dealing with Protovision, he does NOT yet know Protovision's number, he can't download any 'cool games' from that MILITARY system - AND that it definitely IS a military system.
There's no way for him to continue on his path if he knows all this, and there's no way for him NOT to know all this after that extensive research!
Plot hole? You decide, but at least I am sure we can agree that it makes no sense.