consecutive u's

In the continuum of English words, no.

(The OED also turns up "duumvirate", though their latest example of use is from 1894.)

Thank you.

Many are archaic or foreign, and almost half are based on vacuum, but I get more than 100 hits from the OED. In addition to continuum, the better ones include muumuu, residuum, and Weltanschauung. Does pay-as-you-use count?

Not nearly as common as vacuum or continuum, are several -uu- words related to more familiar words:
residual – residuum "something residual"
triumvirate – duumvirate "two-person ruling body"
premenstral – premenstruum "the time during which wise men smile and say 'yes, dear'"