I don't see any resolution settings stored with the app's files or registry entries, but there is an .ini file that tells it to skip the initial splash screen, & if needed the program window can then be windowed rather than displaying full screen -- that seems it would have to be done each time you start the software since it doesn't remember that you want to run it in a window. You'll find the .ini file in XP at C:\Documents and Settings\ [UserName]\ Application Data\ ArcSoft\ Perfect365\ Perfect365.ini -- the 4th line should be bSkip=1 to skip that initial screen. The equivalent for Vista/7/8 should be Users\ [UserName]\ AppData\ Roaming\ ArcSoft\ Perfect365\ Perfect365.ini
Perfect 365 does not use D3D or OpenGL or anything where normally your graphics hardware & drivers might be an issue, though it does use Internet Explorer & Flash... Other than making sure Internet Explorer was up to date, the only related guess I can think of would be to try disabling hardware assist for Flash -- the easiest way I'm aware of is open the default msn.com in Internet Explorer, then right click on one of the ads that uses Flash, selecting settings from the menu. There's only a relatively slim chance that would do anything, but it's so easy might be worth a try. Likewise if you're running AMD/ATI graphics hardware you might try different scaling options in Catalyst Control Center, turn "ITC processing" on/off, that sort of thing.
Note that if you remove Perfect 365 you may have a useless entry in the Administrative Tools -> Services window [the necessary files are removed by the uninstall] -- if you want to remove it, after backing up the registry or performing a backup or whatever precautions you feel are necessary, search in Regedit for "adexchange" [without quotes], & you should get 2 or more duplicate Legacy_Adexchange keys under HKLM\ System\... that you can delete, though you might have to set the key permissions 1st to allow you to do so. You'll also have left over Arcsoft folders in C:\ Documents and Settings\ All Users\ Application Data [ProgramData\ in Vista\7\8] -- C:\ Documents and Settings\ [UserName]\ Application Data [Users\ [UserName]\ AppData\ Roaming\ in Vista/7/8] -- and C:\ Documents and Settings\ [UserName]\ Local Settings\ Application Data [Users\ [UserName]\ AppData\ Local\ in Vista/7/8].
Also note that installation adds a few copies of Microsoft runtime files & 1 needs updated, so head over to Microsoft Update after installation.
Note 3: I *think* that if you want to touch-up, fix, &/or improve facial images, you'll find the best way using Google with the 2 words or phrase: Frequency Separation
It's more work, though I imagine depending on the software you used you could export or save the separate layers as individual images, import them into something like Perfect 365, then import the results back into your image editor to put the layers back together. The problem with touching up skin is it's normally difficult if not impossible to effect the color & texture separately, & that's just what Frequency Separation methods or techniques let you to do so the results don't look like some sort of smooth mask made out of plastic.