I’ve found that when it comes to reading papers, there are two distinct things I look for.
Sometimes, I read a paper looking for an answer. Typically, this is a “how to” kind of answer: I’m trying to do something, and the paper I’m reading is supposed to explain how. More rarely, I’m directly using a result: the paper proved a theorem or compute a formula, and I just take it as written and use it to calculate something else. Either way, I’m seeking out the paper with a specific goal in mind, which typically means I’m reading it long after it came out.
Other times, I read a paper looking for a question. Specifically, I look for the questions the author couldn’t answer. Sometimes these are things they point out, limitations of their result or opportunities for further study. Sometimes, these are things they don’t notice, holes or patterns in their results that make me wonder “what if?” Either can be the seed of a new line of research, a problem I can solve with a new project. If I read a paper in this way, typically it just came out, and this is the first time I’ve read it. When that isn’t the case, it’s because I start out with another reason to read it: often I’m looking for an answer, only to realize the answer I need isn’t there. The missing answer then becomes my new question.
I’m curious about the balance of these two behaviors in different fields. My guess is that some fields read papers more for their answers, while others read them more for their questions. If you’re working in another field, let me know what you do in the comments!
4 gravitons 
When I, as a molecular biologist/cell biologist/biochemist read a scientific paper, only rarely am I looking for a question that the writer couldn’t or didn’t answer (the world is full of those) and only sometimes am I looking for an answer to a specific question. Most of the time, I am reading the paper to find out what’s new in a particular area of research, whether the “new” is new information/data, a new theory, a new direction of research, or a new discovery. The only time I read to find out how something is done is when I’m working in an area of research in which I am unfamiliar with some of the methods. That’s why I’m mostly looking at new rather than older scientific literature.
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I would agree almost word for word. The exception would be that reading a paper then often prompts me to look at more papers to look at their sources for key assertions or for prior research they are building upon, to see if an author who particular impressed me has written other papers that I missed when then were released, or to see if anyone else has addressed a similar question differently.
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I’m no scientist and I don’t pretend to be one. Nor am I a lawyer, tho’ I did graduate from Law School. In law school we were often drilled on “what we’re reading a paper (or case) for”. After reading your post and the comments, it seems these two fields have much in common on this matter.
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