Try a quick search on A2A:
http://www.a2a.org.uk/Particularly if anything comes up under 'Quarter Sessions', 'Sessions of the Peace', 'Petty Sessions'. Try just the surname if it's uncommon enough. Sometimes there's very little information in the index and you need to go to the original info at the record office, sometimes it gets quite descriptive:
Ref: QSF/355/D/4, 1797.
Settlement Examination of Thomas Mackenzie, vagrant :- Born in America; merchant seaman; resided at Leeds with his mother & at Beverley. Has wandered with Christopher Nelson (as QSF/355/D/5) in Holderness & has defrauded Ann Smith of Halsham innholder, for liquor supplied to him.
Usually the quarter session records are for things like settlement examinations, minor crimes such as small thefts (probably the reason one of my Cornish ancestors was held in bridewell and given a whipping!), bastardry cases, 'keeping the peace', illegal gambling or running an unlicensed alehouse (often together). I've also seen early records for slander, which showcase the insults of the time, as in this one from 1718:
Jane Ashton c Geo Clayton for slander saying she was "a scold, prophane swearer, curser, brawler, and keeping a scandalous house for tippling" - articles of exception, depositions.