Everyone who has dealt with audio production knows that quality of the whole bunch of future cds depends on quality of master cd.
How can I check my master cd in order to be sure that there is no errors on it?
I assume you mean bit-errors on the physical medium. The CD format uses a technology called cross-interleaved Reed-Solomon code (CIRC), which adds checksums and redundant data to allow detection and correction of low-level bit errors. Usually, this is handled transparently by the CD player's firmware. Upon detecting errors, the firmware will first try to correct the error using the redundant data. If there are too many errors, it will try to reread the same sector of the disk. Only in the event this fails too, will you see an actual error in the audio data.
If you have wave files that were used to produce the files, then you should be able to rip the tracks from the audio CD and compare to the original files. Beware that the audio CD standard (Red Book) mandates a two second pause so you'll have to compensate for that. You can do this in an audio sample editor by making sure the original and ripped CD start and end at the exact same samples.
Also, keep in mind this check depends on the CD drive used. In addition to scratches, smudges and imperfections on the CD, the CD drive too can suffer from dirt, scratches as well as mechanical problems that cause errors.
Each bit on a CD is vulnerable to dust, scratches, smudges etc, whereas e.g. a USB stick is much less vulnerable to normal wear and tear. I believe your best defense against data errors of your master CD is to keep multiple digital copies on media such as hard disks, flash memory drives and online storage. Each of those physical media can fail, but redundancy is really key.
Finally, I believe most CD pressing companies will accept master audio CDs as files transferred through other means than a physical audio CD. For example, errors in unpacking a zip file with an audio CD image from a CD-ROM is more easily detected than for a 3rd party to detect errors directly on an audio CD.
Don't store and transfer your master audio CDs (only) as physical audio CDs.