But, unlike others, I would have enjoyed the "Picard is Wes' dad" plot that they seemed to possibly be setting up in S1. Anything to make characters look like real people and not perfected caricatures of reality.
Oh, wait a second. There's real people, and than there's THE WORST PERSON IN THE WHOLE UNIVERSE. If Picard was in fact Wesley's Dad, this would mean that Picard had done a lot of unforgivable things that only a person with absolutely no positive attributes would commit. It also wouldn't help the fact that,
A. Beverly had not only cheated on her husband, but also lied to him that Wesley was indeed their son.
B. Picard took no measures to make sure this was just a one night fling and instead chose to go all out on this encounter, despite the fact that she was married to an officer under his command.
C. Picard was the one who sent Mr. Crusher on the away mission that resulted in his death. Not to get him out of the way, but when you consider the fact that Picard had knocked his wife up, been lied to that Wesley was his child, and was sent to his death by the real father who will no doubt get your wife for real, you are the unluckiest person in the whole franchise.
A. No need to lie to Jack. Maybe they came clean, Jack forgave them, and Bev decided it was best to tell Wes that Jack was his father so as to avoid confusing the kid. Based on what we know after S1 this is possible. Obviously it becomes impossible later on when Wes gets the holo-gram from his dad, but I'm looking at it strictly with S1 info. Also, for all we know, Jack and Bev were on a break in the relationship or had an open relationship.
B. Kassidy and Ben show that people still get accidentally pregnant in the 24th Century. Maybe they took precautions and they failed.
C. Picard could have separated his personal life from command and made this decision strictly on professional grounds.
Again, this is obviously not what the series writers intended when we consider post s1 information, but using a "s1 only perspective" there's no need to assume Picard is a terrible person to make it work.