Cleanliness of premises is a pretty open question most times. The standard does require it be "appropriate", so while oil on machines may be OK in a screw machine shop, it would not be in an environment where appearance items are painted, handled, etc.
In actual audits I have seen it vary widely. The auditor I have been with in a TS2 audit the last two days said the only two majors he has written so far have been against this clause - one for a dirty mens room. I had a client almost go over the table at an auditor for slamming their cleanliness after they did a major clean-up - he found a couple stray pieces of steel under a bench they missed, nothing else . I even asked an auditor to write a minor against a client because I could not convince the owner he needed to clean up his shop. I have also heard comments from auditors like "It's a welding shop, it is supposed to be dirty".
If you want to define what clean is in a procedure or work instruction, that may take out some of the guess work. For example, you might have a process that every night the floor is swept, chips picked up, machines wiped down, etc. If not, it will basically rely on common sense and the auditor's opinions.
As for documents, you are not required to cover every requirement in TS2 in a documented procedure. I would recommend auditing all of your documents against practice, and also review the standard against both the documents and the processes to make sure you have covered all of the "shalls".
Hope this helps,
Tom