Electromagnetic hazards.
I've looked at somes articles and I cannot find an appreciable hazard to humans from an exposure to RF radiation. The effect on tissue from RF is heating, which can permanently damage the eyes and temporarily damage the testicles (but a hot bath can do worse). The radiation will become much more hazardous above about 10GHz, especially at 22GHz at a water resonance absorption frequency, and generally for higher frequencies. Fortunately, most towers do not radiate at such high frequencies. I suspect some of the communication dishes do however transmit at such high frequencies, since the directionality of the antenna increases with increasing frequency. These may pose a hazard to equipment and or humans. There was an incident years ago where a jumper's camera fried once while in freefall as he passed a comm dish. The comm dish provided fields strong enough to induce currents in the metal and semiconductor components, resulting in a damaged camera. Notice also the diameter of the waveguide. The waveguide dimensions are comparable to the wavelength of the radiation. A narrow waveguide will generally transmit a much higher frequency. A large waveguide will transmit a lower frequency. I think the real hazard is related to arcing and the subsequent production of x-rays. I believe a transmitter will arc to a person if they stand too close to it. Also, there may be arcing occuring inside the transmitter, which will produce x-rays. This may provide a significant hazard. Arcing will also produce ozone, which is noticable by its distinct sweet humid smell. Some people will say the fillings in your teeth will heat up, etc. This doesn't seem plausible if the surrounding metal is not hot. However, heating of metal on the body or rig and portions of the tower should occur if x-rays are being produced. X-rays will be much more readily absorbed by metal and dense tissue than normal flesh. X-rays are very directional and may be the inadvertant source of much of the urban legends surrounding the hazards of towers. AM towers are a different issue. The absorption of radiation by the body follows the dipole model. Essentially what this model says is that absorption occurs when the wavelength is comparable to the length of the body (or some rational fraction of the wavelength, up to some point). I don't know if hazards exist simply from the small amount of current that flows through the body while on an AM tower, or if the hazard originates from low energy x-rays. The x-ray theory is testable by taking unexposed camera film into various radio tower scenarios. I do have some knowledge of x ray production by equipment that creates VHF and microwaves. X ray production can be a real hazard.
X-rays can originate from arcing and bremstralung or so-called braking radiation from the deacceleration of an electron impinging upon a metal target. Arcing can significantly damage hardware in some radiotransmission systems, and will also greatly increase noise of the transmitted signal. Some systems such as klystrons, twystrons, magnetrons, etc... use something called a crowbar when the transmitter (located on the ground, not the transmitting antenna or stinger) arcs to prevent such damage. Arcing should be uncommon and therefore x-ray production should be uncommon. Tthe power on most AM towers is much lower than a TV tower. The chance of arcing and hence x-ray production should be much, much lower for a low power AM system.
In case you are curious about the skin depth effect, I think the skin depth may be somewhat deeper than a few mm. See for example
http://speech.llnl.gov/thesis/3_2.htm
which quotes a few centimeters to a couple tens of centimeters based on tissue measurements of horses and pigs at microwave frequencies. This seems consistent with the behavior of food heating in a traditional microwave oven.
These are all opinions and are not definitive.