How did the huge dragon skulls get placed in the dungeon of the Red Keep? In the TV series (Season 1) I didn't see any door large enough to accommodate them.
When I moved out of my last house, I had to take my couch out through the living room window (double hung). Basically, I don't think it would be a stretch of the imagination for the servants of the Red Keep to move the skulls into the dungeon following orders from King Robert Baratheon, by opening a section of wall or floor large enough to do the job. In fact, this sort of seems a bit more like Robert's style; heavy handed and gratifyingly disrespectful to the Targaryens.
There are many gaps in your assumptions.
- Just because we did not see the door, does not mean it does not exist.
- Even if no door exists, the skull is possibly a uniquely large object. Doors can be temporarily widened (or sections of wall removed) to accommodate the large skull.
- Robert wanted the skull out of the throne room. There has been no mention of him wanting to keep it. It stands to reason that the dungeon was the easiest place to move it to without Robert having to see it. Thus, it must logically have been easy to bring the skull there. If it required an extraordinary effort, Robert could likely have thrown the thing outside because it was too much hassle (unless someone else really wanted to keep it, e.g. Pycell or a random Targaryen sympathiser)
- Qyburn managed to get his ballista down there too, so it stands to reason that there's a door at least big enough to move the ballista. I doubt that they would've taken it apart and reconstructed it (though it is possible). This is somewhat evidenced by the ballista later being transported in one piece (when Bronn uses it on Drogon). It does have foldable arms (the big bow arms) for storage purposes, so it seems to have been built with the intention of keeping it in one piece.
- You're forgetting about the existence of ceiling doors. We have not seen the ceiling in the dungeon. Assuming that it is customary to store large objects in the dungeon, it makes perfect sense to use a ceiling door, which allows you to use a crane or winch to bring objects up/down.
I'm a big fan of the ceiling door option. It makes a lot of sense, both as to why the Red Keep would have one (using a crane for logistical ease of transportation, similar to how a boat's cargo is loaded) and why we didn't see it.