Minecraft – Mob Spawner not spawning anything

You are standing 32 blocks away. Mobs spawn when you are at least 24 blocks away, but then despawn over time when they are 32 blocks or more away. The other thing is, you're standing at Y = 78. I'm willing to bet that you're within 128 blocks (spherical) of some caves somewhere, which are likely filling up with mobs (there are thousands of spawning spots in caves vs. likely a few hundred in your mob spawner), and they are keeping mobs from spawning in your trap. Between this and the fact that you are 32 blocks away means it is likely that the few mobs that are spawning could despawn before you have a chance to kill them. Finally, mobs freeze (don't move) when you are around 30 blocks away, so unless your pads are small, the mobs will stop walking before they walk off the edge into your water streams, assuming you're using that style of mob trap. This means they will stand up there till they despawn.

Recommendations: use small (3x3) spawning pads, with water streams in 2-block-deep trenches between them, and make it small enough that the mobs are quickly funneled into your trap before they have a chance to despawn. Etho has a very simple mob trap design that is easy to build, expandable, and efficient, and has remained so since he designed it over 2 years ago. I would stand somewhere at least 24 blocks away horizontally, around midway up the spawner and at least 128 blocks away from any caves that aren't lit up. Since mobs do walk around for a few seconds before freezing, with this mob farm, the mobs are funneled into your trap before they have much chance to despawn, so being over 32 blocks from some pads isn't a problem.

Your idle area is 130 blocks from the mob spawner, which is just over the 128 block radius from the player outside of which mobs will not spawn:

You should move your idle area up to at least level 72 if you want to see any spawns at all, but I'd recommend having the idle area at y level 175 if you want to reduce the number of mobs despawning.