Are there any problems with my circuit design?
Simulating the pump: A resistor is not a bad way to model the pump in this case since it will just be on or off.  More accurately it would be modeled as an inductor with series resistance, but I wouldn't bother in this case.  Mind you I'm not sure how much value there is in simulating any of this circuit as it's fairly straightforward to calculate current draw and voltages.  It's actually more accurate to model the valve as a resistor also instead of the diode.  
Why did you put the 50 and 7 Ohm resistors on the emitter side of the transistors?  You should put those on the collector side to make sure the transistors saturate when turned on.  The series resistor would 100 Ohms for the pump ((20-12)/0.08) and it looks like you split it into 50 on top and 50 on bottom.  I don't see why.  You did something similar for the valves, but here you added 1 Ohm and 7 Ohms for some reason.  I think because the valve is modeled as a diode which adds voltage drop.  Just do that the same ways as the pump, and again put the resistance in the top side.  It would be much better if you could use a 12V supply so you can drive the pump and valves directly, rather than using series resistors which will get hot and waste power.  That would require more LED chains, but that should not be a big problem.  
The transistors need resistors at the base terminal as Peter mentioned.
You should include flyback diodes on the valves and pump to avoid damaging the transistors.
The LEDs: Assuming you stay with 20V, the 7 Ohm resistor for the Blue chains is probably OK, but I think the 1.3 Ohm resistor for the Red ones is probably too small.  It's hard to accurately simulate LEDs like this.  I would start with a higher value resistor and measure the current before reducing the resistor value.  Otherwise you might overdrive your LEDs and possibly damage them.  If you use a lower voltage supply, you would need to reduce the number of LEDs and recalculate the resistors, but again, start with higher values until you get actual readings.  Ideally you should use constant current LED drivers, but if you use the resistors, make sure they are rated for the power they will dissipate.  This is a pretty cool LED array designer that might help.