Are there any safety hazards when testing the F-16's fire control radar on the ground?
Yes, and aircraft equipped with emitters have their arcs clearly indicated in their manuals, for example, take this diagram for the A-7E (in pink, the wider cone coming off the radome, the other areas are engine intake or turbine blade-off hazards): 



There are two main ways in which a radar installation can be harmful.



Radar waves

These are the desired emission of a radar and are emitted from the antenna in a well known arc.

Based on this page by the WHO (emphasis mine):


  Military radars are numerous and vary from very large installations, which have large peak (1 MW or greater) and average powers (kW), to small military fire control radars, typically found on aircraft. Large size radars often evoke concern in communities living around them. However, because its power is radiated over a large surface area, the power densities associated with these systems vary between 10 and 100 W/m2 within the site boundary. Outside the site boundary RF field levels are usually unmeasurable without using sophisticated equipment. However, small military fire control radars on aircraft can be hazardous to ground personnel. These units have relatively high average powers (kW) and small area antennas, making it possible to have power densities up to 10 kW/m2. Members of the general public would not be exposed to these emissions because during ground testing of radars access to these areas by all personnel is prohibited. The military also use most other types of radars described below.


The specific risks are listed as:


  Possible health effects
  Most studies conducted to date examined health effects other than cancer. They probed into physiological and thermoregulatory responses, behavioural changes and effects such as the induction of lens opacities (cataracts) and adverse reproductive outcome following acute exposure to relatively high levels of RF fields. There are also a number of studies that report non-thermal effects, where no appreciable rise in temperature can be measured.
  
  Cancer-related studies: Many epidemiological studies have addressed possible links between exposure to RF and excess risk of cancer. However, because of differences in the design and execution of these studies, their results are difficult to interpret. A number of national and international peer review groups have concluded that there is no clear evidence of links between RF exposure and excess risk of cancer. WHO has also concluded that there is no convincing scientific evidence that exposure to RF shortens the life span of humans, or that RF is an inducer or promoter of cancer. However, further studies are necessary.
  
  Thermal effects: RF fields have been studied in animals, including primates. The earliest signs of an adverse health consequence, found in animals as the level of RF fields increased, include reduced endurance, aversion of the field and decreased ability to perform mental tasks. These studies also suggest adverse effects may occur in humans subjected to whole body or localized exposure to RF fields sufficient to increase tissue temperatures by greater than 1°C. Possible effects include the induction of eye cataracts, and various physiological and thermoregulatory responses as body temperature increases. These effects are well established and form the scientific basis for restricting occupational and public exposure to RF fields.
  
  Non-thermal effects: Exposure to RF levels too low to involve heating, (i.e., very low SARs), has been reported by several groups to alter calcium ion mobility, which is responsible for transmitting information in tissue cells. However, these effects are not sufficiently established to provide a basis for restricting human exposure.




Incidental radiation

@Dohn Joe pointed out that a secondary danger of radars, which is actually common to most high frequency energy sources: incidental radiation in the form of high energy photons (X-rays) generated in parallel to the desired radiation. Basically, the process used to generate high frequency electromagnetic waves is not 100% efficient, meaning some energy goes into generating other stuff, like heat, or X-rays. Note that at these energy levels it is often more common to use particle theories instead of waves, since they are the same.

This phenomenon led to a number of health cases in Germany in the 2000s (link in German), when crews who had worked on radar systems in the '60s and '70s without adequate protection developed health complications. Some also passed them on to their children due to genetic damage.

A report dealing with the dosage rates for technicians can be found here. One conclusion that stands out is that the effects and dosage rates were heavily dependent on the position of the operator, since x-rays attenuate when travelling through any media, and while air is not the best shielding material, it does help.

To obtain a rough estimate of how far would this incidental radiation propagate, we can run some numbers. The F-16 has had a number of radars along its service life, but we will use the AN/APG-68 radar introduced in the F-16C/D Block 25 as it is the one with the most readily available information. 

X-ray attenuation follows this exponential formula:

$$
I/I_0 = e^{-\mu \rho x}
$$

Where $I/I_0$ is the ratio of energy after attenuation to the original energy, $\mu$ is the linear attenuation coefficient, $\rho$ is the density of the medium and $x$ is the distance traveled. It is important to know the energy of the emitted particles as $\mu$ is different at different energies. Wikipedia gives the peak operating voltage in the Traveling Wave Tube of the AN/APG-68 as 24kV, which should limit the theoretical energy of any emitted photons to 24keV.

Taking $I/I_0 = 1/e$ we can obtain the distance after which the intensity will have been reduced to about 36.7% of the original. Taking $\mu= 0.56585\,cm^2/g$ (from here, interpolating for 25keV) and $\rho = 0.0012\, g/cm^3$, we obtain $x=1472.7\,cm$. 

This means that after about 15 meters the intensity will have dropped by almost two thirds, and it will continue doing so for every 15 meters afterwards. This is a conservative value, the real distance should be less due to moisture in the air and a lower median energy in the emitted beam, meaning that even if the equipment was improperly shielded, the risks should be limited to people working directly on the radar.