Here are some past paper topics. I'm omitting topics that didn't work out particularly well.

Outline for an experiment concerning synonyms and near-synonyms (the experiment was eventually carried out and published)
The influence of non-English languages on Shakespeare's drama
Middle Low German–Scandinavian contact during the Hanseatic period
Examining European loanwords in Japanese through reviewing print advertisements
Eating from the melting pot: Food-related loanwords in American English
English loanwords in Chinese: Phonetic and semantic borrowing processes
The present and future of Yiddish loanwords in American English
Glottochronology
Slang versus jargon
Why don't we talk like New Yorkers anymore?
English idioms: A complex history
Constructed languages: An analysis of fictional languages in science fiction and fantasy worlds
Etymology of the Internet
West African Pidgin English
Functions of taboo language in drama and song lyrics
The myth of the pure Appalachian dialect
Calliope syndrome (a.k.a. misles)
Arabic influence on Spanish
Tracking loanwords in Yiddish and Ladino through Jewish history
Infuences on the development of Spanish in Latin America
Tracing words used in the Ulster English dialect
The "Lake language": An overview of Mush (a very localized dialect in the Boston area)

Here are some further suggestions. Check back from time to time to see if there are new topics that have occurred to me.

We know from research on the brain that taboo words are stored in the brain separately from other words. Is that also true for slang? Is there even research on this question?
Can we use purely linguistic relationships among words to tell us about society or culture more generally? I'm thinking of how we used the Germanic versus Romance origins of titles of nobility to infer that English society was less stratified before the Norman Conquest than afterwards. Another example would be the names for the months that we discussed in class, pointing to March once having counted as the first month of the year.
African-American English vocabulary - influence on American English more generally
Comparison of how different languages (or dialects) handle new words (say, English versus some other Germanic language, English versus some Romance language, etc.) - borrowing (English potato), compounding (Dutch aardappel, literally 'earth apple'), phrase (French pomme de terre, literally 'apple of earth')
Revolving door borrowings - Borrowings from Germanic into some other language (primarily French, but could be others) and from there into English. Or more generally, from Germanic via some non-Germanic language back into Germanic.)
Semantic change: One-off and idiosyncratic changes in word meaning (i.e. not the general kind, like widening or narrowing of meaning)
Suppletion as a general topic (Are there common patterns across the world's languages?)