I see that posts have an ID. for example if you like a post and then another person reblogs it, it appears as liked by you already. So there should be a way to tell Tumblr not to show in my dashboard posts that I already saw. I've seen this in some internet forums; do you know if Tumblr has this feature?
No, I don’t think that Tumblr’s dashboard offers such a functionality.
Keep in mind that rebloggers may add additional content to reblogged posts. So if all reblogs of posts you liked were hidden, you would not notice when one of your reblogging followers adds content to it.
It might be possible to achieve something like that with an (e.g. Greasemonkey) user script.