I believe that – ultimately – there is no contra-indicated exercise. But there are most certainly exercises that are contra-indicated for any given individual.
In personal training, I assume that a client is properly screened, that the goals of this client are understood, and that the program is designed accordingly. It may be difficult for an outsider to judge the appropriateness of an exercise without knowing all of that.
As an example: when I talk about exercises in general, I often use the triceps dip with full body weight as one that I would not recommend to most people. But the same exercise would be perfectly okay for an olympic gymnast training for parallel bars.
Group exercise is always a dilemma because you have people of unknown medical history, some of them you never saw before. While I would not teach an exercise that is inappropriate for 90 % of all people, I always advise people to listen to their bodies and only do what is right for them.
Similar to Karin, I believe on assessing the client OR the class for each exetcise.
Military presses, for example, are often performed incorrectly. In a personal training setting it is easier to coach an individual to proper execution than in, say, a group of 50. Double leg raises a.k.a. Double Straight Leg Stretch in Pilates are perfectly appropriate in a Pilates class, but may not be for a deconditioned training client with weak abdominals or lumbar spine issues.