You can observe the finish first of all. A true antique will have a few visible bumps and bruises. So an absolutely flawless patina without the slightest sign of age is something that needs to be considered.
Ensure the antique does not smell new! .... sounds dubious but anyway it holds true that an antique does not smell new.
Ideally you should look out for pieces that are not overly polished and re-polished as in some cases too much polishing tends to devalue an antique and takes the essence of the historic appeal out of it.
Look out for any repairs and restorations done. Badly done restoration jobs will again devalue the furniture.
In case of chests, desks etc with drawers check if these glide in and out with ease.
Look at the handles of such drawers and chests for originality. If in case these have been replaced these should be good quality and suit the piece well.
If you are planning to go for tables or seating options you should ideally check out how sturdy they are on their feet. Avoid wobbly pieces as much as possible since restoration can be a little expensive.
If you plan to pick out your piece from an auction, do your homework well since there can be a considerable amount of premium on this price.
It is always better to buy from dealers that are part of some dealers association as these people usually play by strict rules. So you can be rest assured that you will get the best deals on various kinds of antiques.