I used to work in technical sales for a company that manufactured and supplied the stainless steel wire to the nut and bolt makers. Bolts for all industries worldwide from the aircraft engine makers to the chemical industry.
The austenitic stainless steel bolts you will buy in a bolt kit will be fairly soft and low tensile. For many applications that doesnt matter - the mild steel used for most applications is pretty soft itself. However there are some applications where high tensile bolts are used and these should not be replaced by the sort of stainless that you can buy off the shelf. Yes its possisble to make higher tensile austenitic stainless bolts and nuts but these are very much specialist items made for particular applications. Indeed, one of our objectives in making the steel for the bolt makers was to produce something really soft and maleable so they could cold form it without problems.
So if the mild steel bolts you are replacing are in safety critical areas or carry head markings like 8.8 or 10.9 ( ie are high tensile) then dont use stainless to replace them. It isnt strong enough. Just stick to using stainless on applications like holding cosmetic panels on the bike.
Stainless is prone to galling ie seizing in application but this isnt a common issue with well made bolts. If you feel the bolt starting to tighten before its anything like fully home, dont tighten any further. Do the reverse and withdraw it. Run it through a die. Maybe a tap down the hole. What is a common issue is using stainless into alloy castings and then finding 2 years later that they wont come out and when you try, they shear. The problem is that electrolytic corrosion between alloy and stainless produces ally compounds that not only are more bulky than the parent metal ( and therefore make the thread a tighter fit) but they are also the sort of thing you might use as an abrasive. So they grip like a yorkshireman holding a shilling. The solution that I use is to coat the threads before assembly with Duralac, a chrome compound used in the aircraft industry for just this purpose but freely available on Ebay. There is also a Teflon compound..