Langenscheidt, Der Große Muret-Sanders:
Andeutung f <-; -en>
1. cf Andeuten
2. (Wink, Anspielung) hint, intimation, suggestion, inkling, allusion, (bes. versteckte) insinuation, innuendo
Merrian-Webster's Dictionary of Synonyms:
insinuation, innuendo mean covert suggestion or a covert allusion to something. Insinuation applies chiefly to a remark, comment, or question with conveys or seems to convey a hint or implication, often one that is discreditable to the person at whom it is aimed <by tacit agreement they ignord the remarks and insinuations of their acquaintances -- D.H. Lawrence> <we reject any insinuation that one race or another, one people or another, one people or another is in any sense inferior or expendable -- Eisenhower>
Innuendo more often applies to the method of covert suggestion than does insinuation, and when it applies to a definite instance, it is referable to meaningful smiles, glances, inflections, as well as to remarks; in both bases the term definitely implies a suggestion of somthing that is injurious to the reputation of the person concerned <I prefer the most disagreeable certainties to hints and innuendos -- Byron> <in this play Middleton shows his interest ... in innuendo and double meanings -- T.S. Eliot> <"He -- eventually -- married her." There were volumes of innuendo in the way the 'eventually' was spaced, and each syllable given its due stress -- Wharton> <he learned by chance remarks overheard, from innuendo, a dropped word here and there, a sly meaningful snicker -- Harold Sinclair>
In the context given, I would prefer "our teacher dropped a few subtle (or cautious) hints", although Langenscheidt's dictionary seems to agree with hv's train of thought. I consider "innuendo" and "insinuation" to refer more to an "Anspielung" or "Unterstellung". Refer also to the discussion of the two words in Merriam-Webster's dictionary of discriminated synonyms above.