Looking through the debug log for my failed attempt to install picasa, I saw that the installer it uses is called Astrum; see http://www.thraexsoftware.com/aiw/ A free demo of that installer is downloadable from http://www.thraexsoftware.com/download/aiw.exe Predictably, it doesn't run under Wine, either; it also puts up a dialog box at the beginning (which unhelpfully doesn't show any text), and if you click "ok", it just puts up the same dialog box again.
I tried for a while to figure out WINEDEBUG settings that would provide some illumination about what's wrong. Best I came up with was WINEDEBUG=warn+all,+dialog,+text wine aiw.exe > log 2>&1 in hopes I could tell what the missing text was, but no dice.
Given that this is a free-ish installer, and more apps might start using it than just Picasa, maybe it's worth looking into... - Dan
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Dan Kegel