You can try ctrl shift i to access Developer Tools. See these relevant threads: Where do error messages go to die after being displayed?, and Where can i find Logfiles
Another option if the message isn’t there is to press printscreen key when you see the message and review it from the pasted screenshot. I agree that It would be helpful to be able to isolate all error messages that show in the popups. This is especially true if there are multiple in quick succession.
Good luck!