Continuous plot issues
I just watched 2 episodes, the one where they thwart a plane hijacking and the one where guys posing as CIA agents kidnap Murdock to steal a helicopter, for the first time in well over 15 years and few things stuck out that I hadn't really paid attention to. I know the writers intentionally pushed the boundaries of realism, but they're plot issues nonetheless.
BA stands outs in all that gold and, in at least the Murdock abduction episode, wearing all-camouflage clothing. Los Angeles is probably the only place he'd blend in enough not to be recognized from a wanted poster or something. For being fugitives they frequently use their real names. In the Murdock abduction episode Hannibal goes to Rio under his own name. Not John, but Hannibal. In modern shows about cloak-and-dagger criminals and fugitives, they use various identities, rent & own vehicles & properties under one or more of their assumed identities. Perhaps the lower level & sophistication of communication and technology of the '80s as opposed to today is why the authorities wouldn't have caught them.
The other thing I'm curious about is their finances. In the hijacking episode they get $50,000 which Face explained dwindled down to about $256 after putting half into their retirement fund(s), a third into taxes (which BA questioned), insurance, medical expenses, etc. I don't know how or why they'd pay taxes unless it was through a legitimate retirement fund such as an IRA and/or cover identities involving banking. What would they have insurance on? BA's van and Face's Corvette? Medical insurance under cover identities?
(this signature was absent on picture day)