I wanted to add to the conversation, but I'm not sure this is really an answer, because I don't know. We really need a domain expert here.
jquery-mobile seems to be a good tag. jQuery Mobile is a framework. Traditionally, there's been little question that technology tags are good tags. The single question currently tagged with it is using that framework, so I would call that an appropriate use and certainly, there are some experts out there who know this framework very well. These are all hallmarks of a good tag.
I looked at the questions that have both the jQuery and Mobile tags, but I don't see anything that indicates they are using this framework. This is the part where we need a domain expert. Maybe they are and I just don't know that they are. It appears to me that they are using jQuery and Mobile technology, which makes the separate jquery and mobile tags appropriate. I don't believe they should be retagged unless some one with the appropriate domain knowledge does so.
So, as it is, I think the current state of things is okay. Except now we have a "problem tag" that is a hyphenated version of two existing tags. But it's a good tag, and it means something different from what the tags means separately. So.... yeah. Not sure what to do about that... If it stays, I am absolutely positive that it will be mis-used in the future. If it goes, then the other tags will be mis-used to cover this technology.
Hello Rock! Meet Hard Place.
Until the fate of this tag and related questions can be decided, I have added the following snippet to the jQuery-Mobile tag's wiki. Please feel free to improve upon it.
Please do not use this tag for the incidental use of jQuery and mobile technology. This tag is for use with the jQuery Mobile framework only.