Wi-Fi Through Captive Portal Does Not Connect
I found a solution to the captive portal problem with 10.10.2...


Connect to the internet via iPhone and USB cable.
Now also connect to the wifi network with the captive portal. Change the default route to use the wifi.
Now the laptop uses the phone for DNS requests, but routes other traffic via the wifi interface.
Authenticate on the captive portal page.
Unplug the phone and restart the wifi.


With a bit of luck the captive portal should remember you and you should be able to use just the wifi interface.

My best guess is that the DNS setup process fails (no /etc/resolv.conf file) when the captive portal firewall is not letting traffic through. OS X probably does some test to see if it's on the internet (probably tries to reach a URL like captive.apple.com) and if this fails then it just stops setting up the DNS system).