What to do with wrong results in talks?
I either believe this other paper is wrong, or that it is a trivial consequence of my own result


Let me be blunt, if it's wrong and a trivial consequence of your own result, then your result is wrong too. Make up your mind: which is it? Wrong and trivial are not synonymous. The answer differs depending on which applies.

If you believe that the result is wrong.


If you want to publicly humiliate the other researcher, then you can say during your talk that the other researcher's result is wrong. You will not make any friends and will not impress anyone by doing this.
Otherwise, your first course of action is to talk about it with the other researcher in private. Have you even considered that you misunderstood something? Most people are reasonable, and if the result is truly wrong, then you will know how to act based on your discussion. Otherwise, this is a whole can of worms, and the answer depends on a ton of factors.
If for some reason you have not had time to talk with the other researcher, then I would not mention the result at all, and elude the question if asked about it during the talk. If you really don't want to elude it, say that you are aware of a possible contradiction between your paper and the other one and that you are looking into it. (See, that's called tact.) I would also take the opportunity of having the other researcher in the same room to talk about it after the talk, in private.


If you believe the result is a "trivial" consequence of your work.


If you want to insult the other researcher in public, then say that the other word is a "trivial consequence" of your own work during your talk. You will not make any friends and will not impress anyone by doing this.
Or you can simply not mention it at all. If asked, you can say that it's nice to see other people being interested in your own work and finding applications.