At the colosseum, it is really interesting to know that when the gladiators fight in the arena, they have no idea what type of beast it will be and where will it appear from. You can actually see that different tunnels were built for this purpose.
Do get the ROME pass which will cost you about 20euros but offers you unlimited rides for 3 days on public transport and includes entrance to 2 attractions of your choice.
The Vatican city was simply awesome, it is describe as an independent small country within Rome. The St Peter's Square and St Peter's Basilica is truly impressive,the the paintings inside were all masterpiece especially the Dome painting of heaven.
Vatican city stamps are collectables, its common to see tourist buying and sending them back.