I get loads of compile errors
You need to think of Cuke4AS3 as a project running outside your IDE so if you did something in your Flash Builder/FDT/Intellij/Flash Develop project then do it in Cuke4AS3, typically this will be the addition of swc's and other compiler arguments. Put this stuff in the "Mxmlc Compiler Arguments" section in the config tab
-compiler.library-path 'Full path to my swc directory for my project' is your friend
For more on the compiler arguments have a look at Senocular AS3 With Mxmlc or the Adobe Docs

Unhelpful error messages such as "Error #3219":
Go to https://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/runtimeErrors.html

Error: could not find JRE
Error: could not find Java 2 runtimeEnvironment
Set java.home in C:\Program Files\Adobe\Adobe Flash Builder 4.5\sdks\4.5.0\bin\jvm.config to ../../../jre or wherever your jre is

Error: could not find JVM
Try setting the JAVA_HOME environment variable to the location of your jre

Firewall gets in the way
Unblock port, theres a server in there waiting to get out

It just hangs and the debugger shows that it is stuck during invocation of a step definition, then times out
This happens when you have defined exactly the same step in two or more different feature files. Cuke is trying to execute the code on the wrong step object. If you look at the output you can see which actionscript step class is being used to invoke the code so you can check to see if this has happened e.g.

  Background:                       # /Path/to/command-processor.feature:6
    Given a valid command processor # features.step_definitions.CommandProcessor_Steps