The detective approach is to use the "what's new" files from the MAME Previous Releases page
here.
See if there's a ROM from your collection that is listed in "what's new" as being redumped and audit that game to see if it has the newer version.
For example, if a CPS-1 game requiring "TN2J_09.12A" doesn't work with MAME 0.148, but a CPS-1 game requiring "MB63B.1A PAL" does, your set is probably between 0.145 and 0.147 since "TN2J_09.12A" was redumped for 0.148 and "MB63B.1A PAL" was redumped for 0.145.
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The shotgun approach is to start with a recent version of MAME and roll-back versions one at a time until the most number of games comes up working when you audit the ROMs.
Scott