The Dell display will undoubtedly connect to the mini, and work with it, regardless of which model. However, while most of their models will work well with a Mac mini, there have been some which render rather less than ideal results - slightly greyish or fuzzy images.
If the display is a CRT model or an LCD panel which connects via either VGA (analog) or DVI (digital) then it should work perfectly. If, however, it's an LCD with analog-only (VGA) connector, and it is a 15 or 17" model from approximately 2 years ago, you may find slightly dim or blurry output. Still usable and mostly correctable with adjustments to display and MacOS preferences, but not as perfect as other screens.