The holes on that array are too small for those leads. If they were slightly bigger, the added solder mass would allow the solder joint to reflow properly. It also looks like the person that soldered it did not preheat the entire board to assist the solder joint formation and reflow. I can say this because the thermal damage to the PCB is apparent at each of those locations, and I have solved this problem myself by making the hole bigger before, and have even done so on an 0.090" multi-layer PCB.
So, instead of sizing the hole to hold the element being soldered, forgo that for achieving a proper solder joint that does not stress the hole during formation.
Multi-layer boards soak up so much heat that thru-hole parts can be a pain in the ass. The last thing you want to do is undersize the hole and attempt to rely on the device lead to feed the heat through the solder joint or use the hole as a fixturing or location aid for the part. It is supposed to be a specific size *bigger* than the lead, not a tight fit AT ALL, and with multi-layer issues, it should be slightly bigger still. This provides more thru-hole plating on the larger hole, and a bigger annular ring, as well as a larger solder mass.
It will be easier to build, even if it requires a new method for exact placement of the device(s) if that was the goal in making them so tight.
Plenty of space there from what I saw. Bigger holes = easier build, no performance hit.
I figure it is either an array of discreet sensors of some type or a photo-multiplier tube exciter array that one finds under the socket, splitting up 1500 volt feeders. At least, it looks similar to one I used to make. Can't tell though since you are not showing that side of the board.