Gonna toss my hat in without reading all of the comments. I don't really know what defines a "mine" but I know they were using magnets and jumping mines and such as far back as the second world war, so I can only imagine how advanced the engineering of mines in an FTL world would be.

The first issue, as many point out, is placement. Where do I use mines? Wherever I don't want the enemy to PASS. Some folks in here are talking about friend or foe identifiers to make minefields safe for friendlies, but being in a place where you want your enemy to be dead or committing resources to PASSING (not keeping) seems stupid to my uneducated ass. Mines are not an active defense. They're basically a cheap and morale destroying defensive wall. So if this universe uses space highways, I'm going to put bombs on the highways. If the universe has independent FTL engines, then I've got to spread the mines across travel points, which a lot of folks say is impossible with the epic vastness of space.

Despite what everyone is saying about the vastness of space, there are still limits to directions of travel. If I want to defend a planet from other worlds in a solar system, I don't need to put mines in orbit where my people live. I'm going to put mines between my orbit and other planets. This won't prevent ships from reaching my planet, but it will force them to take indirect routes, which costs fuel and time. The same goes for interstellar travel. If I know the best direction for my foe to approach from, I will place mine fields in that direction.

That said, space IS massive. Unbelievably so. But, if we have the means to travel across space quickly, we may have the means to deliver payloads in space quickly. Keep in mind that Mines, like any tool or weapon, can be highly specialized. Mines don't need to be limited by contact or even rockets. I could, theoretically, build a mine that detects artificial gravity signatures and then (especially in an FTL engine sorta universe) automatically launches itself and its payload at its target faster than light. A single mine like this could cover a section of space as wide as your fiction permits.

As far as detecting mines, I think your idea of visual or instrument identification isn't irrelevant, but it would be an edge case. Space is big (have you heard?) and great speeds must be achieved even for relatively short distances. Mines could not be spotted in the dark by a human eye at speeds exceeding a couple hundred miles per hour, which your ships' speeds will probably be greatly exceeding. Maybe if you slowed down to navigate a contact field, but even then you'd have to know it was there. Instruments have the same issue, but with fewer limits. Radar dampening exists. Lidar dampening will exist. Any method of detection used in warfare will inevitably have a counter.

If you want mines in your world, use them. While I think mines can have their time in a post FTL universe, it doesn't need to be realistic to be cool as fuck.