Here are a couple of issues and a proposal how to address it:
Issue 1. Some questions seem to be applicable to multiple SE sites. Sometimes users wonder: should THIS applied math question go to Mathematics or MO or Computational Science or Cross Validated? should THAT computer theory question go to SO or MO or CS or TCS?
Issue 2. Some users are interested in multiple sites, and may want to view multiple site questions w/out clicking though sites.
Solution: consolidate all SE sites into a single one, and assign to each question one or more "supertags" that indicate with which site(s) the question is associated with. When visiting SE the user, instead of choosing the site from the drop-down box, would select one or more "supertags" indicating the sites he is interested in viewing (similar to selection of usual tags on individual sites). The questions ONLY with appropriate supertags will show up. (This is different from handling of the usual tags, which highlights the questions among visible untagged ones; supertags would filter out untagged ones completely).
Solution of Issue 1: the questions applicable to multiple SE sites may have multiple supertags.
Solution of Issue 2: the user interested in multiple SE sites would just select multiple supertags.
I initially posted the above question on Area51, where it was tagged as off-topic because it belongs to MSE. I think my confusion of the appropriate site for this question reinforces the validity of the UI change proposal. :)