My thoughts on the matter have evolved and changed over the last two years. What helped was re-reading antimoon, and in particular this article
http://www.antimoon.com/how/readhow.htm
The basic point is that when you're reading a book or watching TV for enjoyment, your brain is filling in the parts it doesn't understand. As you get better at a language, your brain gets better at doing this. The problem though is your skip or skim over the connecting bits that fills out the language. You read and listen ok, but as you're not good at the "bits" you sound like a caveman when you try to talk.
Now, you can do what the above article suggests and slow down your reading. You put the sentence into a perspective that can apply to you. You change the situation and see if it applies, etc. I consider this turning reading into a studying experience which can be draining.
Now, by putting such sentences into an SRS, you slow down your reading automatically. You decide "Hey, do I really know this sentence". Did the meaning words come across as intended in the sentence? You know what purpose the sentence held in the narrative (Who said to who, atmosphere it was said in, situation it was said it). Of course, after you spent time understanding that sentence (via dictionary or other look up method), will you keep that understanding a week or a month down the line? Hence why I put it in an SRS.
Now comes the complicated part: You can sentence mine for different reasons. The above is what I'm doing in order to 90% to 100% understand a TV show. The assumption then is this over time translates to being able to comprehend other TV shows. In addition, I get a bit more practice in how Japanese is used when talking to other Japanese people.
You can sentence mine for vocabulary. So you grab a sentence that uses a new word in a way you can understand, given a small or even no definition.
You can sentence mine for grammar. You see examples that use ~として in your favorite shows.
You can sentence mine for phrases. Want to know best time to say: あの野郎なめやがって then a show you've seen is best to mine for it.
Then there's how you're using the mined sentences. Are they recognition only, dictation in part or all, partial blocked out, etc.?
Yeah, so there's quite a bit that can be said about sentence mining. Hard to say what each of us are doing with it past the basics.