Running with --jsonrpc-api "web3,eth,personal,parity_accounts" fails to create a new account in the parity web3 console application (via UI):

Reproduced with 1.6.3 on kovan and homestead. However, accessing this via web3 nodejs console, works as expected.
JS console dapp uses :8080 webserver which is not affected by --jsonrpc-api (only :8545 is). You can enable all apis using --dapps-apis-all
It will be addressed by #4474, for now it works as intended.
start your geth with --rpcapi "eth,net,web3,personal"