What are some signs that a therapist may have poor boundaries with their clients?

Disclosing feelings, fantasies, and experiences to the client in ways not related to the work the client is engaged in.

Eager anticipation (or anxious anticipation) of the next session in ways that distract.

Serious disappointment when the client cancels a session.

What is the definite integral of x^x from 0 to 2?

General Introduction to Boundaries from Panahi Counseling:

Routinely going over the time limit with certain patients, compromising the time for the next client.

Struggling with fantasies of deeper connections with clients, whether sexual or parental or other intense or intimate relationships beyond psychotherapy.

Record-breaking cosmic structure discovered in colossal galaxy cluster - Phys.org

Frequent phoning or texting of clients to “check up on them and make sure they’re OK.”

Sense of competition with persons who are important in the client’s life.

Off the top of my ancient head:

Plug Power Stock Is Heating Up On Short Squeeze Hopes. Should You Buy PLUG Here? - Barchart.com

Failing to mention the client in supervision/consultation, out of fear the supervisor/consultant will advise return to ordinary healthy boundaries.

Obsessing about clients outside of work hours.

These items can happen fleetingly, briefly, in any therapy, but if they’re frequent, it’s definitely time for the therapist to get some good, solid supervision/consultation.

James Webb telescope discovers 'a new kind of climate' on Pluto, unlike anything else in our solar system - Yahoo

Session-expressed curiosities about client details not relevant to the therapy.