One sign is when you re-read or re-watch material that you studied a few weeks or months ago and it seems really easy or basic, when at the time it seemed difficult or almost impossible.
Having a sustained conversation without your head hurting is another good sign!
I am six weeks in and the progress seems painfully slow. I often gravitate to vocabulary since that is the one area I can objectively measure progress. I can clearly see the effort of my work (vs grammar, listening and speaking).
A couple "mini signs" I am slightly improving:
I catch more lyrics in the Spanish music I listen to (even when not paying attention).
A native speaker no longer sounds like one long continuous garbled sound (with an occasional gap in an English sounding word like "problemas"). Although I do not comprehend most of the words, I can now hear the many more pauses.
I can catch the prefixes of more verbs in spoken language. This helps me get the "gist" of what is being said. For example, I can catch "cre----" and know its something to do with creer and believing. I still can't catch the tense and don't know if it is past, present or future.
I'd say my listening comprehension has increased from 10%-14% in the last three weeks, but it doesn't feel like a 40% increase!
I like the question and all your answers, and agree totally with all you.
Two months ago, I've started my Skype meetings, and usually I finished with a headache and absolutely sweaty. Despite my English isn't not much better than it was, I feel more confident and less afraid of making mistakes.