These errors indicate that the X server is unable to load the Extended Display Identifaction Data record from the monitor during setup. In practice, this means that X will attempt to pick what it thinks is a sane resolution based on some probing, rather than autoconfiguring to the best setup available for your specific monitor. That you get reports from two different search subsystems is just evidence that X is trying really hard.
Ensuring these messages do not appear is somewhat difficult: it requires troubleshooting precisely why the EDID could not be read (the get-edid utility from the read-edid package may be useful). If the issue is that the EDID is in a new format not yet understood by your computer, then you'd want to file a bug with lots of information, probably first against the read-edid package, after which the solution would propagate to other software. If the issue is that the EDID is corrupt in some way, or otherwise unreadable, you would need to update the firmware of your LCD and/or display controller, which may or may not be supported by your hardware. Whether there exists some firmware that produces sensible EDID is another matter :)
In practice, if your screen is not corrupted, these errors are unimportant. If the resolution is undesireable, you can force a resolution by creating an /etc/X11/xorg.conf file. Start by running
sudo Xorg -configure, and then edit to have your preferred configuration for your LCD. Unless you are very motivated, it may be safer to ignore these errors, as adjusting firmware or agressively testing software-during-development to troubleshoot EDID detection may impact other workflows on your system.
This error is typically observed on all-in-one systems (of any form-factor) where the manufacturer has prepared special drivers as part of the default installation, rather than using standard drivers for the hardware and operating system selected. While the "optimised" drivers can often work around specific implementation issues with the hardware, they unfortunately offer a temptation to work around compliance with common standards as well. Happily, the tendency for systems to be shipped in this condition has been markedly reduced in recent years, as more and more ODMs and OEMs validate their hardware against multiple operating systems.