What does a "[1]+ Exit 1" response mean?

When you use the & at the end of a command in bash, it runs the command in the background. The [1]+ Exit 1 means that job 1 exited with status 1. The number between the [] is the job number, and the number after Exit is the exit status. If no exit status is shown, it means the command exited with status 0.

The reason you don't see this until you run another command is because by default the status of a completed backgrounded command is not shown until the prompt is updated. This means after another command exits, or you simply press <ENTER> on an empty prompt.

Edited:
You also do not need to use the nohup. Bash will only HUP a process when the shell itself receives a HUP. This doesn't happen if you exit cleanly (via exit, or CTRL+D).
However you can also use the disown builtin to make it so specific jobs don't get a HUP.
Lastly you can also set a SIGHUP handler to disown all jobs when the shell gets a HUP by doing function sighup { disown -a; exit 0; }; trap sighup HUP.

Patrick's answer is correct, although Stéphane's point about nohup is important for users with differing versions. However, the significance of the + (plus) symbol was not given. Here, it indicates it is the "current" job. For instance, if I were to submit 3 commands at once as:

$ sleep 5&
[1] 29056
$ sleep 5&
[2] 29091
$ sleep 5&
[3] 29147

Then wait 5 seconds, and hit return, the output is:

[1]   Done                    sleep 5
[2]-  Done                    sleep 5
[3]+  Done                    sleep 5

As Patrick explained, the number between square brackets is an ordered job number. The + is only given for the latest job and the - is given for the job preceding it. All other jobs do not have any notation.