Mulder calls Linda Bowman's office and gets the name of her client and the address of the appointment without even having to give his name or a reason why he wants the information!
How was Modell tried and convicted in 1996 if he only woke up six months ago? 6 months before this episode would be at least mid 1997.
You can be tried in absentia if circumstances require it. In this case, they had no way of knowing when he'd wake up. So that's probably what happened.
The time stamp when Modell enters the sports store reads 9:13AM and yet when Mulder and Scully get to Bowman's apartment the clock reads 9:10AM. Also, Mrs. Bowman's secretary says that she is headed to her 12:15PM appointment; at ten past nine in the morning? She must have had a long distance to travel since she was late for it anyway and they all arrived before her.
Mulder: (on the phone with Modell) Yeah.
Modell: Two words. It's alive. (laughs)
Mulder: I don't feel like playing your game right now Modell.
Modell: Touchy. Look Mulder there's something I need you to hear.
Mulder: Tell it to me in person Modell.
Modell: No, seriously. Listen to me.
Mulder: No. You listen to me. Either you come back here on your own or I drag your sorry ass back on the bumper of my car.
Scully: That's one hell of a plan, Mulder. A serial killer makes us believe that he's guilty in turn diverting the suspicion away from the real estate lady? Well, he had me going.
(Mulder is briefing assembled Marshalls on dealing with Robert Modell)
Mulder: Okay, look. This is all you need to know. Do not trust this man. Do not talk to him. Do not engage him in conversation. Even if he is unarmed, approach him with extraordinary caution and then only with adequate backup.
US Marshall: So what's adequate backup?
Mulder: Adequate backup? Every cop you can lay your hands on.
Young Orderly: So what's this guy's story?
Old Orderly: Cop killer. Regular people killer. General all around waste of skin.
Young Orderly: So, what are you scared of? Guy's a freaking vegetable. I mean, what's he going to do, run over you with his big plastic wheel?
Skinner: I just want to say you did a good job.
Mulder: How's that?
Skinner: Nobody could have figured this out but you. You knew it was Linda Bowman and not Modell. You were way ahead of me.
Mulder: I almost killed my partner.
Skinner: Mulder, despite that, you prevailed. You won her game.
Mulder: Then how come I feel like I lost?
Detective: I think its supposed to be kitsunegari... Fox Hunt.
Scully: Fox Mulder.
Mulder: Well, that's a little on the nose, don't you think?
As mentioned in the episode, 'Kitsune-gari' is Japanese for "Fox hunt" (with "Kitsune" meaning "fox", and "Gari" meaning "hunting").