I have noticed a few recent changes, and I would like to know where you are going:

AND vs OR:
In the web app and the windows app the tag filter (if you select more than one tag) now works as a Boolean OR, not as a Boolean AND which is what we had before. I actually think OR is more useful, but since the iPhone still has AND it makes me wonder what your intentions are.

NOT
I particularly think Boolean NOT would be a very useful addition. With a NOT filter we could easily eliminate all irrelevant actions from the list and have a smaller and more realistic selection to consider. If the basic filtering is OR, then a NOT filter would be very easy to implement. It would simply be a direct inversion of the ORed result - hide the tasks now shown and instead show the ones now hidden.

TAG BAR
In the web app (and the old windows app, v3) we have had a Tag bar at the top for quick filtering. In the iPhone it has always been a menu, and I always thought this was due to the limited screen size. Now I notice that the new Windows app (v4) also has a menu, and that really makes me wonder. What is the intention?

THE IMPORTANCE OF QUICK FILTERING AND REARRANGEMENT
On most lists, especially the Next list, it is extremely useful to be able to narrow down what you see in order to be able to select appropriate tasks without drowning or having to scroll too much. Quick regrouping and quick filtering are two vital instruments, which should be as accessible as possible. Are you really sure it is smart to hide these at these at the bottom of the screen and to have them as menus that you must first click into?

I had hoped that you would be going the other way, and make quick regrouping and quick filtering even more powerful, flexible and accessible, for example:

- have the regroup options as distinct visible single-click buttons instead of as a menu
- allow you to quick filter the Next list not only by the special "tags" but also by context, project, area and goal. This is probably most easily solved by allowing contexts, projects and goals to be tagged freely, and to let these tags be auto-inherited by everything inside them. Then these tags will be visible on the tag filter bar along with the other tags and can be used for quick filtering.
- allow full Boolean quick filtering using AND, OR, NOT in any combination and in any order using meta keys such as alt-click, ctrl-click and shift-click.
- have all tags clearly visible for each individual task on the list

IDEA: "REARRANGEMENT" TOOLBAR
Instead of having to open the menus for tags and grouping every time, would you consider making it possible for us to "pin" them as a horizontal toolbar and leave them visible for as long as we like? (i.e. let us open/close a "rearrangement toolbar" that contains all the grouping options and tags)? This option - to "pin rearrangement toolbar" - could be included in both of the existing menus (if you'd like to keep those menus).