I don't think the browser can "Check out" a document when it is opened
in the browser.

It is the application that checks it out to edit.

I have not tried checking out a pdf  before opening in IE and then saving
it back and manually checking it in.

I would suggest that test as your next step.

It works if you manually checkout and down load the file  to the
system. and check  that back in after adding coments.

But, not if you checked it out. and Edited it , without downloading
the file explictly to your local system!

any help will be really appreciated!

I believe this is a client issue.

It would be logical that IE is not an editor in this case, simply a
reader even though the plug-in, from your description, lets the user
attempt to make changes.

From other sites where pdf's are available, I can open the pdf  in IE and
make changes and print and/or them locally, but not save  back to the
server.

This probably is performing as designed.

That is a known work around for PDF files. I would recommend
documenting this for your end-users. It would minimize calls to your
help desk.

You are correct . This should
definitely be something to do with the client system settings.

For me it opens ( after checkout ) on the Acrobat Professional. And I am
able to add comments  to the PDF file  and check  it in successfully.

While, for some of then even after checkout it opens on the browser .
Those are the ones who cant check the PDF into the sharepoint with their
comments.

Further -
There was a property setting in the IE to get that opend in the Acrobat
Professional . But, that's no help. Still those users  cant get their
comments saved into the sharepoint when they check the PDF in !

Some of the best guess were that - if you are an admin user on the
CLIENT system ( you are checking it from) , it works. But, I foundout
that though this was very close, It was not exactly true ( from my tests
) .

All the above scenarios were from the client systems running Win XP.

Are all clients using the same version of Acrobat Professional and
same version of IE?