There comes a time when an SE might move on from their organisation and either work for the opposition or some totally new employer. Is it a moral question on what you can say and if you can write any analysis about your old product?
Of course, for many SEs, this is probably covered by a non-compete contract, or perhaps under an NDA that you cannot say anything (bad) about your old employer or their product. However where this is not covered by a contract what should you do (and what could you do!)?
Many moral issues are black and white and I would not do anything like the following:
Write a full competitive analysis from your internal product knowledge
List all the bugs and problems that are known to the old company
Hire all the good people from the old company
Share future roadmap or directions of the old company
Demonstrating the old company's product (unless you are allowed to keep their software)
However there is still a lot of wriggling room in this list. Part of an employee's worth is the knowledge that they have accumulated through their working experience. You cannot sign away your right to earn a living (at least not an honest living) so there are many things in my opinion that you should be able to do. These include the following:
Educate new colleagues about strengths and weaknesses of the old solution
Write a competitive analysis based on published product information
Write on forums about published usage of a product
Join the product user group
Work for customers of the old product (as long as this is clear in your contract)
Work with potential partners of the old company
Unless you have specifically agreed not to do items on this list, it is your right to do so. I'd say that you should think twice about doing anything that would require access to product or information that is kept within your old organisation. You should delete any passwords, FTP access, VPN access, demonstration images or information that is of this nature. Keeping this kind of information (without permission from your old employer) could implicate you if any kind of leak was chased up by your old employer.
Also, keep in mind that many industries are actually quite small well networked groups, and what you do or say can well come back to haunt you. Don't burn bridges that you may want to cross again. Many times the company your knowledge is most valuable to is the one you have just left.