If the old bar's groove is worn much at all, it'll flop side to side really easily. My 394xp had a .050 chain on a .058 bar when I bought it (like most all Craigslist 'deals' the seller really thought he was pulling one over... it's always an easy fix to get the saw running good again). It'd cut great for the first half inch or so and then the bar would constantly hang up and keep the chain from cutting. Put a .058 chain on it (dressed the rails at same time) and it cuts perfect. .005" extra side to side slop is definitely noticeable.
Since I mentioned the thing of Craigslist deals, I wonder how many others have had similar experiences. EVERY saw I've got from there is in "good" condition and ready to go. But then I go check out the saw and it's got the chain on backward and I can see the guy tried to cut with it like that. Or the chain is extremely dull and the oil tank is dry. Or the fuel line is rotted out and the saw won't idle or it won't run with less than 7/8 full tank of fuel. Or the their local shop put the chain brake handle on wrong and it constantly engages the brake. Or the throttle cable is all messed up and only goes to 1/3 throttle when the trigger is held all the way in. Lots of stuff like that. "Good running saw, no issues" yeah, riiiiiight. Sometimes there's a box of old parts included in the deal. Like 3 or 4 clutches and 2 carbs... which are fine but the shop couldn't diagnose a cracked fuel line and a mis installed brake lever.