Here's what I see. Codes may differ in your area.
The flex connector to the hot water tank is not coated and protected. It should have a dirt leg to keep particulates from entering the control valve.
There is no valve on the cold supply. Fixtures and appliances should have a control stop on supplies. Check the gas line for a valve/stop also.
The trap primer should also have a stop for servicing so that the house doesn't need to be shut down to repair or replace. That type of trap primer doesn't require a special design of the piping to operate like some others, but note: every time somebody uses any hot water in the house the primer will add water to the trap. Seems wasteful to me to have it on a frequently used water line...overkill for a trap.
The gas connector for the furnace is also a flex line and enters the compartment of the furnace. This should be hard piped with steel and also have a dirt leg. The gray coating also leads me to believe that it is an old brass flex line and has been recalled due to leak hazards. The brass flexies crack and if it is one, going directly into the furnace is a combustion/explosion hazard.
The 2" stand pipe hopefully is also trapped. Can't tell from the picture.
The make-shift trap for the condensate line from the furnace is deep and not a smooth one-piece construction and will get all boogered up inside.
If there is a backflow device and/or a pressure regulator there should also be a thermal expansion tank installed close to the water heater. An expansion tank anywhere on the cold water piping will help, but is most effective close to the tank. And, yes, even with a regulator that has a thermal expansion bypass, the tank is necessary. The 'bypass' feature is unreliable.
That's all I can see for now. More pictures of the flu pipe and surrounding area may reveal more.