Both of your examples still point to a bad DVD, or a faulty/dirty DVD drive, or attempting to boot with an incompatible OS X version.
I did ask for more details, which you haven't provided yet.
Here's some examples of details that will be more "helpful":
What version of OS X are you trying to boot from? Be sure to include the "point" (OS X 10.4.6; OS X 10.6.3; etc)
Which model Mac are you trying to boot? Specific model would be great (not just "MacBook"). The System Identifier from the System Information/Profiler would be perfect.
Also, any other hardware and software information that you wish to supply, such as RAM installed; if you have other copies of your installer DVDs that work better, etc.
If your Macs won't boot from the internal drive, but will boot from an external drive - then it makes sense that both Macs have problems with the internal drive.
Keep in mind that mounting a disk does not necessarily mean that the system will boot from that disk, or that the disk is even bootable.
If you can boot from that same DVD simply by using an external DVD drive, then there must be some problem with the internal DVD drive.
Finally, I've had innumerable times that a DVD disk may not boot, even though everything else seems to be OK. I have often "restored" the bootable installer DVD to an external hard drive partition that I created just for that purpose. Even better, is to copy the DVD (using Disk Utility/Restore) to a USB flash drive. This is assuming that your Macs are Intel models, and not the older PPCs - which don't kindly boot to USB devices.
So, which Macs do you have - and what OS X version are you trying to install? Don't forget provide as much detail as you think I might need.
One more thing - I can mount a 10.8.2 installer on my 2008 MacBook.
It shows as a choice in Startup Disk, and also shows as a choice in the Option-boot screen. However (even though it appears to be bootable) - I cannot boot to that installer - my MacBook is too old, and it crashes when I try to boot to that Mountain Lion installer.
That's why I need more details....