I've got good news: I think I have your solution...
Ok, let's keep working this. You've just seen that when you compare your wifi network settings on your iPad with what's on your OS X machine (the one being used as a Wifi hotspot), the iPad doesn't have all the necessary values populated in its settings.
This is the problem.
The solution is to manually enter in the values that are missing in your iPad's wifi settings. You need to carefully ensure you are inputting all those values correctly. My first suspicion is there's an error in the values you've entered on your iPad's wifi settings. Again, the procedure is thus:
1. Touch the little blue arrow next to the respective wifi signal in Settings>Wifi on your iPad. On your Mac, have the network settings up in System Preferences>Network>Advanced>TCP/IP and then DNS panes. You should have a different IP address on the iPad, but the Subnet Mask and Router values should be exactly the same as they are on your OS X machine. Now, the DNS values and the Search Domains value will be missing. Of course, you said you entered the values in as they appear on your OS X machine.
Check these values again on your iPad juxtaposed against the OS X machine to make sure you didn't make a mistake with the values.
Here's the real solution though assuming the values were all entered correctly (remember, comma in between DNS server values): leave the Search Domains blank because it looks like there isn't really one! That's why it says domain_not_set.invalid. Seems like a canned OS X alert.
So, after ensuring all your values are correct, with the Search domains value deleted and empty ON THE IPAD, try to connect.
I'm confident you'll be able to connect.
If none of this works, some more troubleshooting tips:
1. Settings>Wifi>YOUR WIFI NAME-Touch blue arrow.
2. Touch, at the top, "Forget this Network".
3. Re-input manually... the DNS servers. You may also need to manually enter values for the Subnet Mask and Router values if and only if those fields are blank.
Also, always make sure you restart your iPad if you are having trouble and close applications that are being troublesome by double tapping the home button, then holding your finger on the offending App in the dock, then touching the minus symbol.