What are the pitfalls for new users of DFT?

Using DFT when it's not appropriate

There's a famous quote:

"When you give someone a hammer, everything to them looks like a nail"

Many beginners only know DFT and try to use it on everything, even when the system is small enough to use CCSD(T) or some other method that is more accurate and not too expensive for small enough systems.

Furthermore, many people use DFT as a black box, without knowing in detail how it works, when it works, and when it's expected to fail.

For the transition-metal-containing system in this post, 8 different fairly decent hybrid functionals were used, and the energy gap of interest ranged from -14.6 to +9.6 kcal/mol (a 25 kcal/mol range for a number that was estimated to be at most 15 kcal/mol in magnitude), and only 3 out of 8 functionals even gave the correct sign for this energy gap. For reference, the term "chemical accuracy" means an accuracy of +/- 1 kcal/mol, so 8 different fairly decent hybrid functionals give energy gaps spanning a range of 25 kcal/mol, it's quite bad.

Lessons learned:

• Use CCSD(T) or MRCI+Q if you can. Sometimes CCSD(T) is also bad, but in those cases you'll often know because it won't likely converge.
• Don't just check one functional, because in the mentioned example, one functional gave an energy gap of -14.6 kcal/mol and another one gave +9.6 kcal/mol for the same system. Try many functionals and check to see if they are giving values in agreement.
• Check ahead of time to see if the system you're studying is multi-reference, strongly correlated, or just poorly suited for DFT. For example if you're studying anions, then the "density-driven error" in DFT is known to be particularly bad and you might want to use Density-Corrected DFT.
• Check to see if the functional you are using has been optimized on a dataset containing molecules similar to the one you're studying: Don't use a functional that was optimized only for organic systems, on a transition-metal-containing inorganic complex.
• Perhaps do an a priori search for functionals that are well suited for your system.

Asymmetry of the grid

If you have done calculations using wavefunction based methods (e.g. Hartree-Fock, Moller-Plesset Perturbation Theory, Coupled Cluster) you are probably already aware that the result depends on the choice of basis set. While DFT can seem very similar, it has an additional dependence that isn't as commonly discussed: the exchange-correlation integrals are evaluated on a grid.

The use of a grid can lead to surprising effects that you don't see with wavefunction based methods. For example, many DFT grids aren't rotationally invariant, meaning they can give a different energy for the same molecule in a different orientation. This has proven problematic for studies looking to compare the energy of different conformers without accounting for differences in orientation [1]. These errors can even propagate through to property calculations, such as NMR, where the most accurate analysis protocols depend on a conformational averaging. [2].

Use of outdated methods

Susi Lehtola has given a good answer, to which I would add: Do not use outdated methods. The fact that B3LYP/6-31G* calculations$^1$ are fast and ubiquitous is exactly zero justification to run them for publication-level work. Take care to evaluate more than one functional and search for benchmark studies of related systems/properties to be able to have more confidence in your calculation. In the realm of molecular calculations, one specifically needs to understand the influence of the amount of Fock exchange on the property under consideration. Finally, a modern dispersion/van-der-Waals correction is typically a simple addon to your calculation.

$^1$ a not-so-random example