This sentence contains a dangling modifier. See:

https://owl.english.purdue.edu/owl/resource/597/1/

Suggested change:

Looking outside, it's beginning to rain. ->
When I look outside, I see that it's beginning to rain.

Dangling modifiers are a completely grammatical part of standard English. They are commonly peeved at by style guides, but not by linguists.

http://languagelog.ldc.upenn.edu/nll/?p=2790

Even Pullum, in that post, doesn't go so far as to say that dangling modifiers are a completely grammatical part of standard English. He writes "Do not misunderstand me: I am not saying that dangling participles are always OK... Some dangling participles are definitely cases of bad writing... It would be perfectly reasonable for a writing guide to recommend that such sentences should be avoided." His point has to do with a particular sentence that is being criticized by another writer. It begins "Without detracting from Fowler's point..." Pullum argues that the sentence "falls within the small range of semi-conventionlized [sic] cases that don't sound all that bad to experienced users of English."

While I would avoid "Looking outside, it's beginning to rain" in my own writing, I agree that it certainly meets the standard of "sentences that one might hear in everyday speech" and probably the standard of "sentences that don't cause confusion". My problem with it is based on my belief (philosophical and empirical) that the primary constituency served by Tatoeba is language learners, and that language learners should understand what (good) style guides commonly say. If it's tagged or has comments on it (as it does now) , they can see the discussion and decide for themselves.