Tim Bowen provides some humorous examples of confusing quite with quiet.

Learners often confuse quite with quiet due to the similarity in spelling. This can lead to some quite amusing situations. A pleasure boat trip advertised on the harbour front on the Greek island of Kalymnos appeared to be unusually unpopular until a closer inspection of the sign revealed that it read “Trips to quite clean beaches”. This use of quite for fairly or not very conjures up images of beaches that have a few bits of litter and rubbish here and there but are not really that bad. This is hardly a positive endorsement. Had the author of the notice used spotless instead of clean, the opposite message might have been conveyed. As with certain more 'extreme’ adjectives, quite can have the meaning of ‘very’, ‘completely’ or ‘absolutely’, as in “I’m quite sure she did it”, “They have achieved something quite extraordinary” and “The food in the restaurant was quite disgusting”.

The use of quite to mean ‘fairly’ tends to be more common in British English, whereas in American English it is normally used to mean ‘very’, as in “We’ve examined the figures quite thoroughly”. Quite can also be used before nouns to emphasize that something is unusual or interesting as in “The news came as quite a shock” or “She lives quite some distance from the nearest village”. Finally, there is the use of quite as a response: “I don’t think teachers should behave like that”. “Quite” (meaning ‘I agree’).

By the way, the aforementioned beach turned out to be quite quiet but quite magnificent!