Looting, in general, is a problem. Pick it up as you go if its inherently valuable, certainly... if you can carry it (four assault rifles aren't heavy, but have you ever tried to carry them? Awkward....). Dispose of the body of a lone hitman that hit you at your doss? Just good sense (as is moving out....now.)
On the other hand I have to seriously raise my eyebrow at the 'list' of problem loot. Four AR's, a few frags and a few thousand rounds of ammo? That's a MINIMUM purchase for a starting Gunbunny in most campaigns of mine. Well, maybe not four AR's (that depends on the campaign), but certainly the frags and the ammo. Four four editions I've never had a samurai that didn't have 10k ammo minimum. If running with the 'absolute pro' mentality, cases of guns (so you can discard them after the runs they've been used on) is standard, regardless of time. Then again, I wrote a rundown on teh state of CSI: Shadowrun, so I'm not exactly unbiased here....
Still: If a few thousand rounds of ammo, a couple of frags and some assault rifles is a problem in your campaign what the hell are your characters doing with major mojo and wired reflexes?