I got a letter from a journal editor telling me that they 'would be happy to accept my paper'; the editor asked me to take care of some minor citation issues (I carelessly misspelled one author's last name and I misplaced the publication year of a cited work.) and then upload the final version of the manuscript to the submission system. Although this letter sounds very certain/positive to me. I am still a bit wary and anxious (after all, this is still not a formal acceptance letter). I quickly resubmitted the final version of the paper to the submission system in the same day. It has been two weeks since I heard from the editor and resubmitted the final file. I know that it's impossible to expect a speedy response. But, in my scenario, how long should I wait to write back to the editor and ask for a formal acceptance letter (or is it even okay/appropriate to do this?) At this stage, should I be worried (about any possible hiccups that may stand on the way of getting the paper published)? Thanks very much for your insights and experience sharing.
I agree that you have nothing to worry about, but I slightly disagree with the premises of Anonymous Mathematician's answer. Basically, I don't think there is such a thing as an "informal acceptance letter". Or, to be a bit more precise, I don't consider a distinction between formal and informal acceptance letters to be a helpful or a particularly meaningful one. Rather, the distinction that may be worth making in connection with your situation is between simple acceptance and "conditional acceptance". Another distinction that may be relevant here is between a well-written letter and a poorly phrased letter.
Let me explain: a conditional acceptance is one where the editor indicates willingness to accept a paper conditioned on the author making certain revisions to the manuscript that are deemed to be satisfactory. It may be reasonable to characterize the letter you got as a conditional acceptance letter from a purely logical point of view, but honestly, given the fact that you were only asked to make a couple of changes of a purely cosmetic nature, I would view this as semantic nitpicking. If, as Anonymous Mathematician said, the "informality" of the acceptance means that the journal still has a theoretical option to reject your paper, then I would argue that by the same logic they could do that even with a more formal, or less conditional-sounding, acceptance. After all, it would be no less ridiculous for them to argue that they are now rejecting the paper because you failed to satisfy the "condition" of correcting a couple of typos, than it would be for them to retract a completely formal, unconditional acceptance. If you look around on Academia.SE you will find examples even of such crazy things happening on very rare occasions.
Personally, given the "I would be happy to accept" wording and the modest nature of the corrections you were asked to make, your letter just sounds like a simple acceptance letter to me, which brings me to my second point about the distinction between a well-written and poorly phrased letter: some people -- in fact, rather a lot of people -- use language in a careless or sloppy manner and/or are not sensitive to nuances of the English language such as the difference between a conditional and unconditional verb conjugation. I think it's quite possible that the editor used the conditional tense not as a way to pressure you to submit your revised manuscript faster as Anonymous Mathematician speculated, but simply out of a lack of awareness of how the writing would be perceived by you, the recipient of the letter, and without realizing that the lack of clarity on what would happen after you submit your revised manuscript would result in needless worrying on your part, you posting a question here, us writing an answer to your question, etc.
To summarize: congratulations on your paper being (in)formally and (un)conditionally accepted to one of the top journals of your field! You have nothing to worry about, but to once again differentiate myself from Anonymous Mathematician, I won't tell you that you "shouldn't worry"; it is human and reasonable to worry, and it is human and reasonable to be annoyed at an editor who uses needlessly ambiguous language in an acceptance letter. What I would probably do in your situation is to wait a few more days and, if I still don't hear anything, send an email to the editor politely asking for an acknowledgement that my revised manuscript was accepted and for confirmation that the acceptance is "formal". You may in fact need to do this for your peace of mind, since my guess is that without contacting the editor yourself you may not get any more "formal" acceptance notification than the one you already got. (You will probably get some correspondence from the publisher at some point about galley proofs of your paper, copyright transfer forms etc., which would be an implicit confirmation of the acceptance, but this could not happen for many months.)
You shouldn't worry much. It's extremely unlikely that an informal acceptance will turn into a rejection, although I suppose it is theoretically possible. In my experience, this is something editors do to get leverage over authors: authors are faster and more diligent about making revisions when acceptance has not yet been guaranteed, even when they know it is almost certain.
I wouldn't worry about the two week delay or get in touch with the editor yet. For example, if the editor is in the U.S. the Thanksgiving holiday intervened, and the end of the semester is always a busy time. It's also possible that the editor is checking with a referee (although this may not be necessary for such minor revisions). It can't hurt to ask whether the revised paper was received, but I'd recommend waiting another week or two.
Incidentally, asking you to add citations sounds a little odd. Are these from a referee report, and do they look like important references that you missed? One unethical thing editors are occasionally tempted to do is to pressure authors to add citations to manipulate citation rates. (For example, adding citations to their journal or their friend's journal.) That's not necessarily going on here, but if it is then it's an inappropriate use of informal acceptance to get leverage over authors.