It really depends on how fluent the speaker is. True fluency in a foreign language is extremely difficult to achieve and should not be underestimated. I've discussed this in another context, giving one man's opinion about what a test for genuine fluency would entail.
That said, it is easier to be fooled by someone who has time to compose a written question or answer on this site. That doesn't mean it still isn't hard to "pass" for native fluency, but it's a damn sight easier than writing in chat or submitting to questioning by a cop who just pulled you over for speeding. My feeling is if you wake someone up at 3:00 in the morning and ask them their opinion on the merits of strong drink, it ought to be very easy to weed out the fakes (easier than, say, dodging the fist that may be about to connect with your jaw in that situation).
I see solecisms all the time in the writing of non-native speakers on this site, but I am quite impressed with the mastery of many of them. With one or two exceptions (who will remain unnamed), all the non-native speakers I know of whose gravatars reside on the first rep page here write pretty nearly flawless English. Nevertheless, I will occasionally detect an odd usage or a misapplied idiom, which will lead me to wonder. Mostly I've encountered those only in chat, however, and I've seldom seen any in questions or answers. The clues I'm talking about aren't typos — we all mak those and find them failry easy to detect.
Genuine tip-offs will appear in the odd use of a preposition
He was married with her for 15 years. [He was married to her for 15 years.]
or an infinitive in place of a gerund
The game is all about to hit the ball. [The game is all about hitting the ball.]
or present tense in place of present progressive
I eat now. What do you want? [I'm eating now, what do you want?]
I've made these examples fairly obvious to illustrate my point, but some of the mistakes can be very subtle, and if someone is really capable they can be hard to spot. But even in the best of the best here I will sometimes get a faint tingling as my Spidey sense warns me that someone may not be a native speaker. Oddly, hyper-correct grammar may be another tip-off. There are certain mistakes people make that actually convince me that someone is, in fact, a native speaker. Practically nobody who grew up speaking a European language, one that has clear markers for cases, would ever say "Jennie threw a party for Bill and I." But you can encounter such mistakes every day at any mall in America.