I just finished tipping over the dishwasher to replace a heating element and I noticed the plastic around one terminal was melted and and charred; the area around it was also charred. The wire was no longer connected; it appeared to have been burned off. The other terminal and wire looks fine.

Could a bad heating element have caused this? If so, what are the risks of simply replacing the element? What else should I consider?

Thank you,
Ken

Here are your parts
Replacement parts for WHIRLPOOL GU1200XTLQ3 UNDERCOUNTER DISHWASHER | AppliancePartsPros.com

I am not sure what you are measuring when you say "the round coil terminals"

The heating element should be 10 to 30 ohms.
When elements fail they usually just go open or burn up in one spot and open.

Make sure that the connections to the element are clean and tight.
Any corrosion/pitting/dirt is a resistance and when electrical current flows through this connection it will heat up. This degrades the connection further, generating more heat etc., etc. till the connection fails.