This is mostly repetitive, but I look at it all as an odds game.
First, there’s no “sure thing” either way. The wine in a perfect-looking bottle can still be corked most obviously, but also cooked or otherwise flawed, and the wine in a bottle with numerous physical condition issues can be great.
Thinking of examples from my own cellar, I had a cooling unit drain hose plug up one time, causing nice cool water to drip onto bottles below and then onto the floor. By the time I noticed and figured it all out, several of the labels were permanently water-stained. Obviously the wines inside were totally unaffected (and opening them has borne this out). Likewise with label tears. Particularly with oversize bottles (Huet and especially Turley come to mind), the bottles can be a tight squeeze in some racks or bins and get torn as the bottles are inserted or removed. Again, obviously, this has no effect on the wine.
So generally speaking I pay no attention to label issues. Same with depressed corks which seem not to have any correlation to poor storage.
The others are all odds games. I would “never” buy a bottle where the fill level is half-way down the bottle, but even there I put “never” in quotes because I’d pay $5 for a 1945 Mouton with that fill level if I knew it was genuine. I expect lower fills the older the wine is, so where I’d start lowering my max price depends on the age of the wine, but generally I’d view the age-adjusted fill level as one that might change what I’m willing to pay rather than one where I’d not be willing to pay anything.
Ditto for seepage or raised corks, especially when other evidence points away from abusive storage. For example, riesling or producers known for over-fills as mentioned above. Also, older mags which (or so I’ve often been told) were often hand-filled and thus often over-filled. Likewise, a multi-bottle lot with only one seeper or only one raised cork to me indicates a higher chance that the bottles weren’t all kept in an attic in the summer. So I might avoid a 3 bottle lot where all three have lots of seepage, lower my price on a 3 bottle lot where two have modest seepage, and be willing to bid full price on a 3 bottle lot where one shows very mild seepage and the other two show none.
I also view these issues as cumulative. I’d much sooner overlook a raised cork OR seepage OR a somewhat lower than expected fill level than I would overlook all three on the same bottle, for example.