It is very common for published papers to have still minor errors. Some are sometimes even introduced during the publishing process. So yes, submitting a paper with errors is common too. When submitting to a conference with website closing at a precise time, I do check (and find) errors up to the last minute.
Errors can be irritating to the reviewers. Generally, if they are minor and rare, they are not a cause for rejection, but can be a catalyst. Take a borderline acceptable paper. When the reviewer has 10 of them to review fast (for a conference for instance), it can be accepted if error-free, and rejected (with basically the same content) if containing a proportion of errors.
Clean papers are generally appreciated, reviewers may feel the authors have done some effort to help them review.
As it is difficult to re-read again a paper that you have written, suggestions:
- use your co-authors generously, make them explain to you the theory you have written,
- use your colleagues, friends or family, they can have a critically eye on what you cannot see anymore, notations undefined, etc.
- read the paper backward, aloud.