The schematic doesn't show the Arduino and more importantly, how it is powered. Any variation in the Arduino Vcc will show up as noise in the ADC results, unless you are using a stable external ADC reference.The schematic also does not show the required capacitors on the 7805 regulators. There is no need to use more than one 7805 to power the sensors. Note that if the 24V supply drops significantly, so will the individual 7805 outputs (by up to 100 mV), and that also shows up as noise in the ADC. See the 7805 data sheet for the details. You would be better off not using the 24V supply for either the Arduino or the sensor power.
Do you really mean PWM frequency, or do you mean the duty cycle, as set by analogWrite()?
A pot MUST be powered from Arduino's 5volt supply to keep it's ratiometric behaviour.The voltage output of a TMP36 should NOT be measured with Arduino's potentially unstable default Aref.A 47ohm gate resistor could cause dips in the Arduino supply (~ 75mA gate charge/discharge spikes).Depending on the gate charge of the mosfet.Leo..
I don't understand what you mean by "how to connect the grounds". They must be connected by wire, to establish a zero voltage reference.If you are contemplating alternative circuits, post them so we understand the question.
Make sure that the high current to the electromagnet does not flow along the same wires as the sensor's grounds. This is usually called a 'star' grounding layout where each device is wired back to a common point - they don't share any length of wire.
In order to achieve this, there has to be some some common point at which the ground wires connect so that one wire can be routed to the ground pin of the Arduino. Are you saying to do this as close to the ground pin as possible?