I'd agree with Hypothesis. I found that going off on tangents sometimes sparked off my interest in related ideas and got me excited about my research again, when I was in a rut with it. It felt like an elaborate form of procrastination sometimes, but by the end all the tangents, or blind alleys as you call them, had either fallen into place in my overall thesis or given me ideas and material for post-doc projects or got used up in teaching, so none of it was wasted.
The only possibly problem with spending too much time on these things depends on where you are with your timetable. If you're writing up then it's probably not a great idea to go off in too many new directions or you'll never get the thing submitted. If you've got the time, I'd go down as many blind alleys as you want, it's unexpectedly exciting sometimes!