I don't think any of the claims in this quote are serious problems, and many are not even problems at all. The whole quote seems to be an attempt to describe perfectly reasonable things as if they're somehow terrible.
There is a giant pile of bugs called "QA Notes"
This is mostly true. Although they aren't all necessarily bugs; many are more like enhancement ideas. I think it's good that there are accurate records of all the ways the software could be improved. It's a sign that the company has high standards and good documentation, and is actively trying to make its software even better.
It's unrealistic to expect that highly customizable software involving millions of lines of code will be perfect in all situations. So yes, there are quite a number of situations which have been identified as possible issues. But the software still works well enough that many, many people are happy with it.
in some random old code
The company was founded in 1979, so there is indeed some older code. I wouldn't say that the code is random, since all the code I've seen is certainly designed with some definite purpose in mind. I suppose that the code might appear random to someone who hasn't seen it before, since it takes some time to understand what unfamiliar code does.
which you have to fix
Some development time is, in fact, spent fixing existing issues which have been documented. I'm not sure what the author of this quote is expecting out of a software job?
The funny part is one bug generates - 15 other issues, because you don't even know what else might break.
If this happens to a developer regularly, then I would say that he/she isn't doing his/her job very well. Occasionally, unforeseen consequences do happen as a result of a fix. However, most of the time, the consequences are preventable if the developer spends the time to understand the problem, to understand what calls into the code that was changed, and to do a sufficient amount of testing before submitting the fix.
Did someone say unit-tests or integration tests - well there are no automated tests.
As another commenter already stated, this is false.
you have to finish X bugs & Y projects in a Z days and if can't - Sorry you're fired - Bye Bye.
All companies have expectations for what employees are supposed to accomplish. This is the way the world works.
If the performance standards are objective, then some employees tend to complain that the standards are unfair because they don't take into account the individual circumstances of each situation. If the performance standards are subjective, then some employees tend to complain that the standards are unfair because they are based primarily on how much management likes you. Again, I don't know what the author of this quote expects as an alternative.
Or that you deal with no interesting CS problems?
At a software company, your job is to make good software. Occasionally, this involves solving interesting CS problems. More often, it involves doing what the customer needs, which may or may not involve actively expanding the boundaries of your computer science knowledge.
There are other careers which involve solving interesting CS problems more frequently (such as research scientist or professor).