Let's get this out of the way - a cheap quartz watch will keep better time than the best mechanical watch. So what should be my accuracy expectations for mechanical watches? There are many subjective opinions about this, much of it misinformation. So rather than impose our own subjective opinion to the reader, lets just go by facts published by the people who actually make these watches:

From the Omega FAQ:

"The majority of watches that do not have a chronometer certificate have average precision tolerances of between -1/+11 seconds per day.

The precision of a mechanical movement depends on the individual habits of the wearer and can therefore vary. A qualified OMEGA watchmaker can adjust the precision of a watch to within the OMEGA tolerances."

https://www.omegawatches.com/customer-service/faq/

So from Omega's own website, NEW non-chronometer Omega watches ON AVERAGE can have a variance of as much as +11 seconds per day. It is also directly implied that if an Omega watch does not fall within these tolerances, it does not necessarily need a factory service - it may just need minor adjustments from a watchmaker.

Another way to look at this question is to review the accuracy of ETA mechanical movements, the kind used in Omega watches:

ETA movements require 95% of a produced lot to perform within the following parameters:

Standard 
- adjusted in 2 positions: CH and 6H (click HERE for details on positional timekeeping terminology)
- average daily rate: +/- 12 seconds
- maximum positional variation: 30 seconds
- isochronism between 0 and 24 hours: +/- 20 seconds

Elaboré
- adjusted in 3 positions: CH, 6H, 9H
- average daily rate: +/- 7 seconds
- maximum positional variation: 20 seconds
- isochronism between 0 and 24 hours: +/- 15 seconds

Top
- adjusted in 5 positions: CH, FH, 6H, 9H, 3H
- average daily rate: +/- 4 seconds
- maximum positional variation: 15 seconds
- isochronism between 0 and 24 hours: +/- 10 seconds

Chronometre
- adjusted and timed per COSC specification (see above link under Standard) which is not much different from Top Grade

So depending upon the grade used, a plus or minus 15-30 second variation is normal for a NEW ETA movement, with a small percentage having variances greater than this. This is before adjustments from a watchmaker