Platform: Windows 7
Build: 9567

I was able to replicate this bug. Pressing shortcut for "Save As" multiple times in quick successions causes multiple Save as dialog boxes to appear.

I was able to only get up to two dialog boxes appear at the same time. This occurs only when "Use OpenOffice.org dialog" option is unchecked. 

When shortcut is pressed with "Use OpenOffice.org dialog" option checked then one "Save As" dialog box opens and at the same time Special Characters dialog box appears.

Here are some tests that I performed:

Test 1
a) Open Writer
b) Click shortcut for "Save As" multiple times in quick successions (with "Use OpenOffice.org dialog" option unchecked)
Result: Two save as dialog boxes opened at the same time.

Test 2
a) Do the same as test 1
c) Type the same file name in both boxes
b) Click save button on both dialog boxes
Result: No option for file exist appears when save button on second dialog box is clicked.

Test 3
a) Open Writer
b) Click shortcut for "Save As" (with "Use OpenOffice.org dialog" option unchecked)
c) After a few seconds Click shortcut for "Save As" again (with "Use OpenOffice.org dialog" option unchecked)
Result: Only one save as dialog box is opened at the same time. An error beep sounds when "Save As" shortcut is clicked 
the second time.

Test 4
a) Open Writer
b) Click shortcut for "Save As" multiple times in quick successions (with "Use OpenOffice.org dialog" option checked)
Result: One save as dialog box opens and at the same time Special Characters dialog box appears.

Test 5
a) Open Writer
b) Click shortcut for "Save As" (with "Use OpenOffice.org dialog" option checked)
c) After a few seconds Click shortcut for "Save As" again (with "Use OpenOffice.org dialog" option checked)
Result: One save as dialog box opens and at the same time Special Characters dialog box appears.

Additional Information:
Test 2 is informational and test 3 passes, the results for the rest are unexpected. The same tests were also performed with same result for Calc, Draw, Base and Impress in build 9567 and Writer build 9582. The same tests were performed on "Microsoft Office Professional Plus 2010 (Version:14.06 32-bit)" and Firefox 10.02 and 
only one dialog box opens in all cases. The Microsoft Office test was done on Windows XP.

User Impact:
The opening of more then 1 save as dialog box can cause confusion in users of whether when their document was saved or whether it was saved or not.

getting rid of value "enhancement" for field "severity".
For enhancement the field "issue type" shall be used.

Bug confirmed.

Pressing CTRL+S I was able to open up to 3 consecutive Dialog Boxes

CTRL+SHIFT+S = same bug up to 3 consecutive open Dialog Boxes

CTRL+O =  same bug up to 3 consecutive open Dialog Boxes

CTRL+P = only 1 dialog box opens no matter how faster you hit the shortcut

SHIFT+CTRL+N = only 1 dialog box opens no matter how faster you hit the shortcut

M.-

(In reply to LadyMariu from comment #3)

Confirmed on Windows 7 & 11 with version 4.1.12