Is the resin pot on the same height or higher than the part? In this case resin will flow into the part by itself which results in pooling.
Keep the resin pot lower, and maybe don't fully open the line if needed.

The unevenness in bag tightness is quite normal

Basically, once the resin begins to flow, the inlet side will only be at the ambient pressure of the incoming resin.  

Once the whole set-up is clamped-off, the negative vacuum pressure closest to the exit port will begin to equalise across the surface of the part. I don't think that this alone would cause issues with surface quality once cured and everything should tighten-up after infusing

If you suspect that your part might be infusing too quickly, you can (if not already using) create a 'resin-break' just ahead of your exit line. This involves cutting your flow media short of the exit edge to leave a gap of around 20mm or so before another strip of flow media along that edge of the set-up that the exit port sits upon. This should help ensure that all areas of the part have enough time to wet-out prior to the resin starting to travel up the exit line and help slow things down a little. This is especially helpful on small-ish moulds

Leaving the inlet port open for 30 seconds after clamping the exit to let-in a little more resin should also help to make sure that there won't be any dry spots

No resin gasses off only at the flow front where the pressure is low. The resin break, while being a very good thing, does not do anything for your problem...

In that case, it's possible that the inlet side is being a little starved of resin and it's more likely if your part is quite small. 

Try doing things the other way around and leave the inlet port open a little while after clamping the exit. Assuming that everything's air tight, I wouldn't worry too much regarding the looseness around the inlet, as things will consolidate well once the vacuum level equalised after close-off and any excess resin will likely be removed along with your stack materials