What are Heavy Metals?
Heavy metals are constituents of the earth's crust, naturally-inherent since the time of earth's formation. Heavy metals can also be discharged by industry, in addition to their natural sources.
As it relates to the safety of the food we eat, the questions surrounding heavy metals is less about whether or not they are present. Instead, the questions become:
1. How do heavy metals become present? More specifically, what percent of heavy metals are sourced from industry versus nature?
2. In what amount are they present? This translates to:
a. What are the established tolerance limits (safety thresholds)? and
b. How does the amount present compare to that limit (how real is the threat) in the food we eat?
The technical definition for heavy metals is "metals with a density greater than a certain value, usually 5 or 6 grams per cubic centimeter."
Heavy metals (in relation to food safety), refers to those metals of high density, regardless of their source, as being hazardous. Not all hazardous items are metals, and so the term "hazardous elements" is used where both metals and nonmetals are described. Further, not all hazardous elements are likely to be found in food products. 
To better explain, let's take a look at the periodic table of elements (see Figures 1-4):
Figure 1. Periodic Table of Elements, Categories: The shaded portions represent three categories of elements: metals (light orange), metalloids (light green), and nonmetals (light blue). 
Figure 2. Periodic Table of Elements, Density: The portions outlined by the thick, black line represent those elements with a density of 4.5 g/cm3 (rounded to nearest tenths place) or greater. Since a density of or greater than "5 or 6 g/cm3" is recognized as a heavy metal, 4.5 g/cm3 was taken into consideration as rounding rules would meet the minimum 5 g/cm3 density cut-off.
As you can see, the identified density includes elements across metals, metalloids, and nonmetals. Heavy metals would be those elements shaded in light orange and that fall in the area surrounded by a thick, black line. 
Figure 3. Periodic Table of Elements, Heavy Metals: The shaded portions in yellow represent those heavy metals that are at-minimum measured in food products. It is standard procedure in food production that these key heavy metals do not exceed their tolerance limits for food safety purposes. These are identified at-minimum on specification sheets* between parties handling food products. *See below section, "Due Diligence." 
Figure 4. Periodic Table of Elements, The Elements in Food: The shaded portions in yellow represent those elements (regardless of metal, metalloid, or nonmetal) that are naturally-occurring in food products, falling under "ash content," more specifically, "minerals" on a Nutrition Facts Panel. Many are optional for the manufacturer to list, but those required include Calcium, Iron, and Potassium.
Heavy Metals In Food (Q&A):
Now that we're on the same page with what we're talking about, this is how it relates to the food you eat.
1. Heavy metals and hazardous elements (sometimes referred to as "toxins") are leeching into the foods we eat.
This is true. Heavy metals and hazardous elements can enter foods via farming and processing practices. For example, they can enter plants through soil and water (generally natural sources) and processing from equipment handing, storage, and packaging (industrial sources).
In supplying a solution that acts for consumer safety, the question is not if they are present, but in what amounts and from what source. To elaborate, heavy metals and other elements are only deemed hazardous if present in certain amounts. A number of organizations and accredited laboratories share their expertise in the form of tolerance limits in published report