This is almost the same wiring as my new system except I'm using an Arduino in place of the PID to control the heating and pump. I have a few suggestions.
If you have not already purchased the switches, you do not need to connect both sides of the contactor coil through the switch. You can connect the one side permanently and then simply use the switch to activate the coil. It will only save a few bucks but it's something. Also you don't really need 240V coil contactors, 120V will do the same but again, this is only if you have not purchased them and want to save money.
The indicator for the heat should not be plugged into the coil. Doing this will illuminate the light whenever you have the switch on regardless of if heat is being applied. I would tie it to L2 that is going into the heating element. This way, if the PID is turning the element on, the light will go on.
I am also confused about pin 2 on the PID. Usually the fuse goes on the hot side.
Be careful using different size wires. I would have a breaker attached to L1 after your first contactor that is appropriately sized and powers the pump and PID using the correct wire size for the breaker.
For the fuse on the pump. I am assuming you are using a March or Chugger pump. These generally draw 1-1.2A so a 10A fuse may be a little large to protect it. I am using a 2A slow burn fuse. This allows the pump to draw a little more current upon start up without blowing the fuse but protect it against damage if the current draw is above 2A for a continuous period of time.
I'm not sure why everyone likes to use the emergency buttons wired the way you do. I have seen it many times and it is on almost all of the wiring diagrams on here. If you are using a contactor to provide the power for the panel, why not use the emergency stop button to cut power to that? I have mine wired in series with the main on/off switch. It is a normally closed button and when pressed, the contactor is disconnected and power to my panel is cut off.
Those are some of my suggestions. I see no reason why it would not work the way you have it, but if you want to save a little money and protect it a little better in case something goes wrong I would make those minor changes. Good luck! Be sure to post pictures when it's all done.