First of all, Photoshop and Lightroom are fully color managed applications that will actually use the monitor profile to display the image.Many other applications (viewers/browsers) are not and will just ignore it. So there's a difference right there.
That said, when you get that message in Photoshop, it means exactly what it says. That profile is bad and should not be used.
The real solution is to use a calibrator to make a new custom profile for your monitor. Until you get that up and running, use sRGB IEC61966-22.1 as monitor profile. You set this up in Control Panel > Color Management > Devices:
