1) The computer in your room has a Root Beer Tapper-style holotape you can play, so don't forgot to eject it and take it with you to play whenever you'd like. This is the only hidden item I could find in the vault that you can miss. I don't believe #2 applies to this.
2) If you're looking to maximize every second of play, pick up your PipBoy and then you can literally sprint to the exit. There is absolutely nothing else hidden off of the beaten path, and all of the introductory items you see presented to you on tables (clothes, CAMP, first Perk card, etc) will be instantly put into your inventory once you exit the vault, even if you don't pick it up. You just need to go to your PipBoy and apply your Perk.
EDIT: According to a couple comments, there may also be a holotape recording in the Overseer's office that I may not have ejected myself, but I still guarantee there is no USEFUL loot in the vault that you will miss by sprinting to the exit.
These may not mean a lot to most, but may be helpful to someone, so I thought I'd share.
© Post "Two quick tips for people starting tonight that I haven’t seen mentioned yet" for game Fallout.
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