There’s a longer list of abbreviations for the LSJ on the TLG:
http://stephanus.tlg.uci.edu/lexica.php
or Perseus: http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Afrontmatter%3D5
You can access the TLG lexica without a subscription, but I think you need to register (for free). On the TLG version of the LSJ there is a handy button that says “Show Abbrev.” for any entry.
That won’t help you with unabbreviated Latin like rei (for example in c. gen. rei=cum genitivo rei, “with the genitive of the thing”…in contrast to c. gen. pers(onae) with the genitive of the person). You might find this tutorial helpful:
Relatedly, see this handy list of mainly Latin abbreviations in critical apparatuses, some of which overlap with those used in dictionaries: http://udallasclassics.org/wp-content/uploads/maurer_files/APPARATUSABBREVIATIONS.pdf
For naughty words the whole definition is sometimes in Latin (eg βινέω, πυγίζω, εὐρύπρωκτος, ψωλή, ταῦρος III, several words defined as pudenda muliebria or membrum virile (female and male genitalia)). Or just avoided by “sens. obsc.” (=sensu obsceno, with obscene sense). The abridged versions for schoolboys often remove even these Latin workarounds. In those cases you’ll want a more recent dictionary, especially if you’re reading Aristophanes.