Quite easily; you look at them. If there were a way to programmatically define a good logo, there wouldn't be so many bad logos. I don't mean for this to sound facile, but it is like looking at art, or writing: it is very difficult to create a meaningful definition of what good is, but it is often very easy to classify things as bad and not-bad (if not good and not-good).

It probably isn't worth spending $$$$ on logos. But you should care about design as an extension of caring about UX. If your design taste is sufficient that you can produce a simple, acceptable logo - great! If it isn't, it is possibly a warning sign that you need to involve someone who does have that design taste - and not just on your logo.

To head it off at the pass - yes, some start-ups have succeeded with weak design (although far fewer than you think - simple is not necessarily weak), but start-ups have succeeded under all sorts of circumstances. It doesn't invalidate the principle that a good user experience is very valuable to any product.