Thanks for the dump hint - I could use it.
Well I have not been able to track down the exact cause of the problem, but at the end I have succeeded to see the pictures even on the Mac. Initially , because I tested the HTML code against Safari/Foxpro/IE9 with success and the PC's received it as a mail perfect with the pictures , I ruled out the code.
After sending it with various different parameters for 7-bit coding , multipart/alternative; multipart/mixed, with and without alternative ascii-text , etc. and having no change of the problem (in one instance Mac stuck the pictures at the end of the mail instead of having it as attachement - but never displayed inside the page) I thought about the HTMLcode again (the mail small but was consisting of a cluster of multi nested tables, where in the pictures where placed). I started from scratch with one simple table and one picture - and saw it also on the Mac, so repeated reconstruction every table layer and picture with testing each step again - and at the end - it worked all. So my conclusion is that the mentioned browsers and windows mail are made more HTML fault tolerant for little code mistakes than mac mail. It seems that when forwarding the page from windows-mail to Mac mail , windows even corrects and thats why then it was seen ok on the Mac.
I think that a number of people had similiar experiences. I contacted one advertising company (all Mac freaks and only Mac's there, they do a lot of Internet/Intranet design and develeopments for large companies) and asked them wether they know of any hints or problems - they simply said forget it it's not possible - which is not true - but seeing the HTML correct in all browsers doesn't mean it might ok for the mac mail.
Well any way I now know where I am and know where to look if suddenly a picture is not shown anymore...
Thanks for the help and all the best.