I have been going back and rereading my novels in anticipation of publishing them and discovered I tend to use the words "seemed", "seemed to" and "seems" a heck of a lot. Sometimes it's within the same paragraph or consecutive paragraphs. I hadn't realized how pervasive it was in my stories until the editing and am certain my editor will highlight it as well.
I haven't done any research on this but I imagine others might fall into this problem as well. By the very definition of writing in third-person, you are looking through another character's perspective. So when they interact with other people, they are interpreting what the person is doing or meant to say. So to them, things could seem to be a way when not necessarily being that way. This is true in the real world as well.
For example, you might see someone with their eyes closed and think they are sleeping. So the person "seems to be sleeping." But in reality they might simply be deep in thought. That is how a third-person writer might approach perspective scenes.
But in reality, at least the reality I've written, "seemed", "seemed to" and "seems" while allowing one to stay in the mind of the character decreases the certainty of the scene. If they are seeming to do something, then they might not be doing it. That's fine if that is the intention, but if it's a third-person omniscient point where the other character is acting, then it's far more effective to just have the person do the action.
For example, one could easily write: "But this man seemed different" when the third-person narrator is speaking about something. And that sounds grammatically correct. It could be that the man was different, or he might not be.
However, if you then change it to "But this man was different". You are stating in the definite that he IS different. If you follow it up with the sentence, "he didn't have the same amount of hair or laughed at all of her jokes," then you are defining how he is different. In this context, "seemed different" would mean a completely different statement as in the narrator wasn't sure whether he was different. If that is your intention, then fine, but as I've gone through and reviewed my writing, I've discovered the affirmative is far more relevant than the speculative.
Of course if you do find yourself using "seemed", "seemed to" or "seems" a lot, and they are relevant, to avoid hammering the verb into the reader's skull, it would be wise to switch it up with synonyms like "appears" or "looks".