Of course you can measure customer sentiment. You can even measure the correlation between your brand name and a selection of happy words as they appear on Twitter.

What you should probably not do, however, is elide the essential difference between these two measurements. Twitter is not a representative sample of anything but Twitter. Much of Twitter is spammers and shills, not customers. A lot of Tweets aren't even from humans. And people can mention MongoDB without knowing the slightest thing about it, and I am sure many do. I'm doing it now.

where we agree then, i think, is the fact that Twitter's just another datapoint. and from a statistical perspective, it cannot be considered representative of the wider population for any number of reasons, not least the fact that it's observational rather than a random sample.

that said, it's an interesting proxy for examining questions of sentiment, and its predictive ability has been examined several times academically within specific contexts (elections and markets - e.g. this one by Cornell http://arxiv.org/abs/1010.3003) and found to be relatively accurate.

so agreed, it's not representative. but that doesn't mean it's not interesting and potentially useful.