This can be a AWT or SWT problem. Evaluation is needed.

A simple SWT-AWT testcase DialogTest.java demonstrates the following issue:
A Frame is created as SWT_AWT.new_Frame(new Composite(shell, SWT.EMBEDDED))
Than JDialog with JTextFields are added to a Frame.
When Frame is displayed and gets a focus - the inner JTextField does not get a focus!
When user switches to another app and then back to this testcase the inner JTextField does get a focus as expected.

A similar testcase written entirely on AWT works as exoected. See DialogTestPureAWT.java. Both testcases are attached.

This can be reproduced JDK6u23 and JDK7b131.