Another problem of word vectors is that any word might actually have multiple senses, while vectors are just point estimates. If we wanted to be correct, we needed first to find the right sense for each word in a phrase and only then assign the vector. There is research in "on-the-fly" word vectors that adapt to context, but it's much harder to use.
A third problem of word vectors is out of vocabulary words and words with low frequency. For OOV, the usual solution is to create character or character-ngram embeddings that can be used to compute embeddings for new words. For low frequency words we usually ignore them (apply a cutoff).
Then there is the problem of phrases and collocations - some words go together, such as "New York" and "give up". The meaning of the phrase is different from the sum of the meanings of the component words. In these cases we need to have lists of phrases and replace them in the original text before training the vectors, so we have proper vectors for phrases.
By the way, one amazing tool that goes with word vectors is the library 'annoy' which can do similarity search in log time. So you can do approx 1000 lookups per second per CPU even if the database contains millions of vectors, pretty good. Annoy can be used to find similar articles, or music recommendations. Another remark - my preferred word vectors are computed with Doc2VecC (a variant of doc2vec with corruption). Doc2VecC seems more apt to discriminate between topics, but the secret is to feed it gigabytes of text.
Playing with word vectors has taught me intuitively how it is to navigate a space of high dimensionality. It feels different than 3d-space because each point has a shortcut to other points, each point leads to hundreds of other places which might be far apart. It's like a kaleidoscope where a small change can create a very different perspective.
doc2vecC: https://github.com/mchen24/iclr2017