Bugs
My agility training rooms linking together causing all dwellers sent to any agility training room to get stuck in the uppermost agility room - only 2 dwellers can actually receive Agility training in my Vault at one time due to this!
Dwellers will sometimes equip an outfit restricted to the opposite gender whilst exploring the wasteland
There are bugs relating to the item library, where already discovered items may disappear and undiscovered items appear. Also common items are often marked as 'New' despite being discovered long ago
I have seen occasions where I have been able to equip dwellers with 50 stimpaks by sending them to the wasteland just a raider attack is beginning. This causes them to re-enter the Vault while remaining equipped with 25 paks, allowing me to resend them equipped with a further 25
Flaws
Weapon values not consistent, eg enhanced sawn off worth less than sawn off
Dwellers changing outfits when exploring the wasteland reducing their Endurance
Having to select items individually for sale - bulk sell option required
Dwellers generated by the radio room are always of lower value than births - this diminishes the purpose of the radio room once the number of dwellers gets above 100 or so
There is little or no visual distinction between regular and advanced versions of outfits leading to accidentally selling enhanced outfits or losing them in the vault due to being unable to identify it once equipped
Improving the Vault door actually has a negative effect. It causes the raider attack to last longer as it takes them longer to enter the vault. Beyond the second day of playing, the raiders are easily dispatched once inside and having the attack last 1 min longer is annoying.
The 500 cap prize for the last card in the lunchbox is a disproportionately poor reward compared to the legendary dweller / weapon / outfit prize this should be increased or abolished
Suggested improvements
A record of each dweller's family tree would add an interesting stat screen and make pairing up couples easier.
An improvement to the breeding process could enhance the game. Varying the starting stats of the child based on their parents stats to allow more scope for selective breeding.
A full inventory off all items including items that are currently equipped, to allow you to locate rare items which are equipped but not clearly visible.
Give us more stats! I want to know how much of each resource I have collected, how many creatures I have killed, births, deaths, items collected etc. give us a screen that shows all this.
Let me know if you want me to expand on any of these points.