Dropbox and Text files -- OS X doesn't play well

Here's the situation.

I have a textfile on my Dropbox. I open, edit it, and close it via various devices, including an iPhone, iPad, Windows PC, and Mac with OS X Lion.

Only my Mac gives me problems.

Here's what happens:
1) I make changes to the text file in some device that is not my Mac.
2) Next, on my Mac, I control-click on my text editor's icon on the Dock, and I see the file in the list of "recently used" list of files.
3) I click on this text file's name.
4) It opens up some old version of that file. E.g., if the file name was "myNotes.txt", it will open up a file named "myNotes (deleted 9weri090w09e8rw).txt". And it opens this file from a hidden location that seems to be the local cache of Dropbox's deleted files.
5) Text editors I've tried so far: textEdit and textWrangler.

I know that one of the persistent issues with the OS X is that Applications do not behave in predictable, consistent ways. I also realize that Steve Jobs had anal issues with cross-platform software and may have asked Apple engineers to deliberately create problems for people like me who also happen to use Windows PCs.

Nevertheless, I'm okay with all this because I've figured out workarounds for all the typical problems.

But I can't seem to fix this situation. What can I do to fix it?