What's wrong with HDMI? I have seen comments in various posts here to the effect that HDMI is to be avoided.
Can anyone explain what the problem is with HDMI, and why it's a bad thing?
More specifically, I have a 2nd monitor with three inputs: HDMI, DVI, and VGA. I'm currently using the HDMI port, connecting directly with the HDMI port on my Mac mini.
Is there any reason why I should use some sort of adaptor from one of the Thunderbolt ports to the DVI instead?
HDMI is an AV (Audio/Visual) interface that is designed for consumer devices.  DisplayPort is focused on the computer industry.  As such, one functions better in a compute environment than the other.
Founders and Industry Adopters/Supporters
HDMI:

The HDMI founders were Hitachi, Panasonic, Philips, Silicon Image, Sony, Thomson, RCA, and Toshiba. Digital Content Protection, LLC provides HDCP (which was developed by Intel) for HDMI. HDMI has the support of motion picture producers Fox, Universal, Warner Bros. and Disney, along with system operators DirecTV, EchoStar (Dish Network) and CableLabs.

DisplayPort:

DisplayPort (DP) is a digital display interface developed by a consortium of PC and chip manufacturers and standardized by the Video Electronics Standards Association (VESA). The interface is primarily used to connect a video source to a display device such as a computer monitor, and it can also carry audio, USB, and other forms of data.

One was developed by consumer electroncs manufacters and supported by movie and television studios as well as cable service providers.  The other was developed by PC and chip manufacturers with standardization provided for by the long standing VESA.
This is further reiterated by PC World article from 2019: HDMI vs. DisplayPort: Which display interface reigns supreme?

Though you’ll find it [DisplayPort] alongside HDMI on most late-model, high-end video cards, as well as in Macs and laptops marketed to business users, it rarely appears in Windows PCs aimed at consumers. It’s also rare as hen’s teeth in consumer electronics devices.

Empahsis mine
Your Mac
Your Mac has been using DisplayPort whether it was the native mDP (mini DisplayPort), the Thunderbolt (1, 2 or 3) port or the USB-C port in Alternate Mode.  Only a few Mac computes had native HDMI ports (i.e. Mac mini).
So, going from native DP to DP is going to be the most reliable connection.  There's no conversion.  No conversion = higher reliability.
Converting the Signals
The signaling of HDMI and DisplayPort are very different.  It's not just re-aranging the pin outs of the display signals, the voltages and the presence/absence of a clock sync all contribute to the reliability of the signal.

DisplayPort was designed to replace VGA, Digital Visual Interface (DVI), and FPD-Link. The interface is backward compatible with other interfaces, such as HDMI and DVI, through the use of either active or passive adapters.

Yes, you can convert a DisplayPort signal to HDMI, but I don't recommend it.  Again, no conversion is better, but if you must use HDMI, use an active adapter because it recreates the actual HDMI signal including the clock signal.  A passive adapter cannot do this.

My Opinion on HDMI
Personally, I find HDMI very flaky especially when it comes to audio.  On every single HDMI interface (non-computer) in my house, regardless of how new or old the equipment is, audio will drop out.  The fix is to switch to another input and switch back.  Apparently, it gets out of sync and the switching of inputs &quot;re-syncs&quot; it.
From a computer perspective, in the office, we've had mixed results.  Some computer to HDMI connections work flawlessly.  Others only get a blank or blue screen.  I resolved it by getting active adapters.
However, my greatest experience came when trying to convert a MacBook with a broken LCD (re-purposing a student computer) for a digital signage project.  The 55&quot; Television only had HDMI and I simply couldn't get the MacBook to talk to the TV properly.  I had to get a PC with a video card with HDMI to make it work and at least twice a week, I had to reboot it because the signal became corrupt.  However, the Mac that I had attached to the Dell monitor via DisplayPort ran for months without issue - the only reboots came when we had to apply updates or change the content.