A better map, IMO, can be found in the book Star Trek: Star Charts by Geoffrey Mandel.
...As some might notice, the map in Mandel's book is just an evolved version of Christian Rühl's map here. Or a sort of parallel evolution from common origins: Christian put the real stars on that 2D frame, and two different fits of Trek features were then done on the frame.
Mandel was just able to insert a few last-minute datapoints, say, from the first season of ENT, to come up with something a tad less at odds with the onscreen reality. The later seasons of ENT then went and contradicted Mandel's map anyway.

Plus why does it not have Trill in Federation space? It's a UFP member
But is it? Such a thing has never been stated on screen. Also, the secret about the biological nature of the Trill wouldn't stay secret for long if Trill really were a member.
The only canon data on the location of Trill would be from DS9 "Equilibrium", but that doesn't help much. All we learn is that at some point of the journey from DS9 to Trill, there are still 37 hours to go at whatever speed the Defiant is maintaining - probably as high as possible.
..how areas of space are coloured as if it were a country
That's probably exactly how the Klingons or Romulans would view their holdings. It's all theirs, even those empty spaces between star systems where no Klingon ship has ever bothered to travel.
How the Sol system is nowhere near where it actually is in the Galaxy
Not really a problem with Mandel's maps, either these new ones or his previous try from the eighties.
Shouldn't it be ...
Delta | Gamma
-------------
Alpha | Beta
?
Why? From the usual vantage point of "galactic north", the galaxy rotates clockwise, so
Beta | Gamma
-------------
Alpha | Delta
would be the most "logical" setup if one thinks in terms of spirals. Only mathematicians and electrical engineers really prefer the counterclockwise direction...
Yet there's no real reason to use a spiral setup for a square grid. It's not as if this grid in any way reflects the spiral nature of the galaxy anyway. (And really, for all we know, the names have some obscure origin like the stellar-type litany of O B A F G K M does, not alphabetical at all.)
Timo Saloniemi