If you don't have MAME configured to accept multiple mice, it won't work properly.
Depends on what "properly" means. I'll bet he'll be happier with -multimouse disabled.
Mame 0.61 and mame 0.120 have many differences in the options, so they will need separate mame.ini files (if they don't already). One that hasn't changed is the -mouse option. Make sure it is enabled in both versions.
0.120 has the -multimouse option, 0.61 doesn't. The -multimouse option enabled "splits" the mouse type input devices so mame sees each separately. The -multimouse option disabled "combines" all mouse type devices so mame treats them as one, just like the windows desktop cursor, and older versions of mame that didn't have the -multimouse option. Since you have 0.61, disabling -multimouse ("multimouse 0" in mame.ini for 0.120) will make both version act the same.
If you've tried what's been said on using mouse devices in mame, I'll just be repeating it, but...
Enable mice by changing "mouse 0" to "mouse 1" in the mame.ini file. If you don't have a mame.ini file, type "mame -cc" at the commandline in the folder holding that mame. (repeat for other version of mame.)
More help will need more info on your setup (and what you've tried if you don't want us to tell you to repeat them).