Unlike most of the other people on this forum, I have to say that I don't think the mines are overpowered or completely broken. I've been playing games on medium sized galaxies against 2-4 hard AIs. The mines are omnipresent and they do slow down the pace of conquest. I would argue however that that is the point.
In order to counter the mines, simply set your fleet engagement range to "Hold Position." Then, remove your scouts from your fleet and move them to mine clusters. The trick is not to move them to the mines (because then sometimes they walk right into them), but instead click in the area of the mines. The scout will park itself in the middle of the cluster, de-protecting them and giving you the ability to destroy them with abandon. This works particularly well with fleets well endowed with strike-craft support.
Fleets that lack strikecraft in great numbers can still accomplish much the same goal again by setting the fleet engagement range to "Hold Position." Make sure you have 5-10 scouts in your fleet, and then move it very slowly across the gravity well. Your heavy cruisers, LRMs and other such ships will auto-engage the mines as they are deprotected by the scouts, clearing them as you go. You MUST, however, move slowly. Simply clicking across the well is a good way to get your fleet crushed.
All that said, I do think that the current mine management system is unwieldly and too micro-intensive. I would suggest the following simple fixes to make the situation dramatically better:
1. Increase the radius of the scout's mine detection field by about 25-50%. It shouldn't be so great that it can cover a significant portion of the gravity well, but it also shouldn't take more than one scout to deprotect a cluster of mines.
2. Create a new fleet behavior mode called "Mine Patrol" or "Formation Combat" or "Defensive Formation" or something. In this formation, all ships move at half speed and never break formation to engage enemies. They always auto agress any enemy unit within their radius. Most importantly, scouts are moved in the formation to the perimeter of the formation (rather than at the center/rear where they currently reside). This allows the fleet to detect mines further away from the ships and engage them without necessitating constant micromanagement or manual movement of scouts to mine clusters. All the player would need to do is select the fleet and advance to the relevant area. The mines would be cleared on the way. (Enemies would be able to counter this by attacking the scouts preferentially; they would be vulnerable because they would be to the outside of the formation).
I would suggest also that this formation maximize anti-strikecraft covering fire for the fleet (configure your AA ships to cover the flanks and forward approaches against strike craft, rather than clustering all the AA ships together). This formation would also have useful implications for fleet combat, in that units would never pursue targets. Instead, they would engage any units that came into range with full force (since virtually all ships would be in firing range once the enemy got close enough), and ignore the other ones. (This would be advantageous when the enemy has mines and defenses you want to stay out of range of, or if you're trying to cover your siege frigates, but would be disadvantageous if your enemy was using LRMs or other stand-off units to engage your fleet, or units that do a lot of splash damage).
3. I would consider adding a new scout behavior that would cause the scouts to move towards dense clusters of mines automatically (without actually moving to a particular mine and setting it off). It would be an auto-cast ability that would cause the scout to fly towards mines and deprotect them. Once those mines were destroyed, it would automatically move to the next target. This behavior would be most useful when one is not using "hold position" or "mine patrol" formations but wants to still soften up the minefields of the enemy.
4. Add a very slow decay rate to mines built in a system that is no longer under your control. Make it something like 1 HP every two seconds. If I remember right, mines have somewhere around 110-120 hp. This would mean that they would last approximately four minutes before finally failing. (you could obviously make this longer or shorter if game balance required it). This allows mines to hamper enemy movement in areas not under your control, but might limit nuisance mines (the kind that end up in systems well back from the front later in the game). Historically, minefields do require regular maintenance to maintain their potency, as mines break down, wear out or simply drift out of position. If you wanted to get really cute, you could make the mines undergo radioactive decay, wherin they would have a half-life of 4 minutes or so. (so 100 mines behind enemy lines would on average become 50 after 4 minutes, 25 after 8 minutes, 12 after 12 minutes, 6 after 16 minutes, etc.) That would simulate the tendency for mines to fail, but it would also accurately portray the fact that not all mines do fail, and sometimes mines remain operational well after their intended use. They still dig up old mines and bombs from world war II in Africa and Europe, and they are still as dangerous as the day they were laid.
I think these modifications or other modest changes would make the mines useful as a tool for slowing an enemy advance, but keep them from seeming too overpowered or ridiculous. It would be relatively straightforward for attackers to deal with mines (if not that rapid), but it would be equally straightforward for defenders to counter the attacker's anti-mine strategy.
I'm agnostic as to the suggestion other people have made vis a vis making hte advent mines cost resources. I've seen a lot more vasari and TEC minefields and my commentary is more geared towards what I've seen from those factions. It seems to me however that a little cost would make sense given the extreme expense of TEC mines and the ease with which they can be destroyed by a carefully prepared fleet.
I'd love to hear feedback. Any thoughts?