You're right the solder joints don't look pretty. You should grasp the wires and wiggle them to see if they stay attached. It appears that you could easily have cold solder joints. If this is the case then they will sound bad and be unreliable. You may need to purchase a Weller gun and reflow the solder joints.
I agree with Scotty. Sometimes with speaker terminals if you've got an adjustable soldering station like a Hakko 936, I just turn the temp all the way up as the brass speaker posts need to be fully heated up and then
solder should be applied, or else you end up with cold soldering joints which are unreliable and sound awful. A Weller soldering gun is also a possibility like Scotty said, although somewhat awkward to use into a smaller enclosure.
Do you have anybody around you who can double check your work?