So the verses go like this:
21: Slaughter a lamb.
22: Put blood on the door and stay inside.
23: [Why?] The blood will prevent being smitten as God smites Egypt.
24: Do this in future generations too.
It seems pretty clear that 22 and 23 go together; the reason for putting blood on the door is because God's smiting Egypt. But God is only smiting Egypt this year, not future years. Ergo, 24 -- "do this in future generations" is referring back to 21. Yes, it needs a little bit of forward-scanning and back-scanning.
You were not the first to catch this! The classical commentary Ramban (Moses Nachmanides) says exactly this:
AND YE SHALL OBSERVE THIS THING. This refers to the Passover-offering
itself, concerning which He had said above, and slaughter the Passover
lamb, even though it is removed [by two verses from here]. It does not
refer to the putting of the blood [upon the lintel and on the two
side-posts, mentioned above] in the verse nearby, since only in the
Passover of Egypt were they commanded to do so, [i.e., to put the
blood upon the lintel, etc.], as it is said, For the Eternal will pass
through to smite the Egyptians; and when He seeth the blood upon the
lintel, etc. Similarly, the expression, and ye shall keep this
service, means the offering of the Passover. A similar case [of a
Scriptural expression that is connected with one that is far removed
and not with the one nearby], is the verse, And also unto thy
bondwoman thou shalt do likewise.
The Passover sacrifice is mentioned several other places in the Torah, and it's clear that the blood-and-door thing was only for in Egypt. (In fact, the Talmud tallies the ways that "Passover offering of Egypt" was the same, and different, compared to "the Passover offering of generations.")
So Year One Passover had blood on the door; as long as there was a Tabernacle or Temple (the next millennium or so, very roughly speaking), there was a Passover offering without the blood on the door. Today's Passover seder does not feature a Passover offering (in fact, we don't even eat any kind of dry-roasted meat, to avoid anyone even thinking that we're having a real sacrifice outside of Jerusalem) of any kind, and thus certainly doesn't have blood on the door.
As far as why no Passover offering is brought in Jerusalem today, that's a separate question. (There are a lot of technical obstacles from a strict Jewish-law perspective, and it's also not seen as politically feasible at the moment.)
The Talmud actually notes that when there was a Tabernacle or Temple, the blood (caught immediately from slaughter) was placed on the altar there, then the meat taken to a nearby home or inn for consumption. Thus the doorpost actually served as a decentralized altar of sorts in Egypt. After the Exodus, worship was more centralized. (So practically, by the time the slaughtered lamb made it to your house/hotel in Jerusalem, it wasn't dripping blood anymore.)