Have very much the same issue
InstallError | | 2036 | Error while validating installer for package 'Adobe Flash Player'
since last update to version 26. Circumvented by having changed the extension of the downloaded installer package to .exe and executed it.
Windows XP SP3 (or is it 4 actually by now?)
Log files attached here
[moderator: added 'WinXP SP3' to title]
We are having some issues installing online installer on Windows XP machine. We recommend you to install the offline installer posted under 'Still having problems' section on Installation problems | Flash Player | Windows 7 and earlier page.
Branched to a new discussion topic due to issue being unrelated to topic posted to.
The ongoing issue with the online installer is fixed. You can go ahead and use the online installer for installing latest version of Flash Player on Windows XP.