Electricity, it can actually only be used for two things?

Good question. Well, let's see:

Light via fluorescence - neon tubes, fluorescent lights, LEDs, Lasers (solid state and gas), Xenon flash tubes, etc. where electricity causes electrons to elevate to a higher orbit or leave it entirely, and then emit photons when they fall back. Any heat produced is only secondary and highly undesirable.

Electrolysis - current flow causes ion flow, which causes H2O to break up into oxygen O2 and hydrogen H2. Heat and magnetism are only undesired side effects.

Electroplating - current flow is used to cause ion flow (positively charged metal salt particles) in a liquid in order to cause metal to plate out onto a surface.

Just about any semiconductor and most vacuum tubes - electron flow causes amplification or nonlinear behavior. In all but a few specialized vacuum tubes and semiconductors, magnetic fields are only a secondary, unintended thing. Heat, again, is a secondary and undesired side effect. This category alone covers thousands of devices, at least.

CRT oscilloscopes - electrostatic fields are used to deflect the electron beam, not a magnetic field. To be fair, the cathode normally does use heat to release electrons.

A solar cell does not use heat nor does it use magnetism.

A photocell (resistor that responds to light by reducing its resistance) does not use heat or magnetism, either.

An LCD display does not use heat or magnetism. The backlight is either LEDs or fluorescent, and the LCD panel uses electric fields to change the transmission of light of each color pixel.

Electrostatic speakers rely entirely on electric fields.

Static electricity generators use only electric fields to generate their high voltages. Although the motors are usually electromagnetic, you can use any power source - turn it by hand, use water power, wind power, etc.

Your own body seems to rely only on electric fields and current flow, with heat and magnetism as unintended side effects.

If I took more time, I could probably come up with a few more.

Electrolysis, similar to already-mentioned electroplating, doesn't generate heat - or at least only as a by-product during chemical reactions.

A handheld device for measuring light levels, wind speed, moisture in soil etc. do not produce heat or a magnetic field.

All electrical devices create a magnetic field - current down a wire is a magnet (albeit a rubbish one unless you orient it the right way) - but you can't say that they all fall into the category of statement (2) if it's not intentional?

Perhaps the statement should be modified to read 'electromagnetic field'.

Electricity is only one form of energy. An electric heater converts electricity to heat; a loudspeaker coverts electricity to sound (yes, through a magnetic field, sometimes - remember there are electrostatic speakers, too). Electricity converted to mechanical is the job of motors (also, but not always, magnetic in nature). Electromagnetic waves cover a range of applications from radio, infrared, light, microwaves, UV, X-rays and gamma rays, thus lightbulbs create light energy, xray machine, xrays, etc.

Well, you have left out the entire transmission of information by electrical means although you might feel that electronic (Radio Frequency RF) transmission is subsumed in your magnetic field category.

And actually, since we are talking about little bitty electrons, doing what they do is a pretty good task.

One right off the top of my head is metal plating as in silver plating. The current is not used for heat or magnetism, but rather to move the metal ions.

TexMav

Our entire body and indded, our "being" is electrically motivated. No heating or magnetic fields involved.

This is why studies such as an electrocardiogram work, by detecting these electrical signals.