Fixing the illness directly, not the symptoms
The black boxes usually occur alongside the error:
Overfull \hbox (3.14159pt too wide) in paragraph at lines 41--42
This usually means that there is too much text being rendered in a single line of the output PDF:
|The quick brown fox jumped over the lazy doggie. | <-- boundary
|This is the rendered output PDF of a TeX document.| <-- boundary
|This cannot fit on one line without being squashed.| <-- overfull!
|Unfortunately, if TeX made a break before "being" | <-- boundary
|and "squashed", it would look weird. | <-- boundary
One way to fix this is to simply reword the paragraph causing the issue so that TeX can make a line break in a visually pleasing matter. Often, this merely involves removing or adding a few words until the issue disappears:
|The quick brown fox jumped over the lazy doggie. | <-- boundary
|This is the rendered output PDF of a TeX document.| <-- boundary
|This can fit on one line without being squashed. | <-- FIXED!
|Unfortunately, if TeX made a break before "being" | <-- boundary
|and "squashed", it would look weird. | <-- boundary
Addressing the symptoms instead
Of course, one can change the tolerances, at the cost of looking less aesthetically pleasing. If we set \sloppy, the result might look like:
|The quick brown fox jumped over the lazy doggie. | <-- boundary
|This is the rendered output PDF of a TeX document.| <-- boundary
|This cannot fit on one line without being | <-- UGLY
|squashed. Unfortunately, if TeX made a break | <-- UGLY
|before "being" and "squashed", it would look | <-- UGLY
|weird. | <-- UGLY
Instead, if we set \overfullrule=0pt, as described in @egreg's answer, the Overfull \hbox error is silently swept under the rug, but our text still goes over the boundary and/or is overly squashed together, as shown in the first example.
Content and presentation are intertwined. Sometimes we must compromise a bit of one for the other.