Can an employer send all the particulars to other employees as to why you were fired and use the internet to do so?

There could be a potential defamation claim here if the person is harmed somehow. However, truth is a defense to defamation. NM may have specific laws against this and there may be privacy implications. Consult with a local attorney who handles employee privacy matters.

What is legal and allowable and what is just in bad taste and unprofessional can sometimes be too different things. Although my colleague talked about truth as a defense to defamation there could be another issue here with interference of future employment if a possible employer was looking at this person to hire them. Most attorneys will advise businesses to only confirm whether an individual worked for the company, their title, and length of employment, and not to go into details to prevent defamation liability. However, if the cause of the firing reflects or affects the reputation of a company (ie its stock, etc.) it could be a reason for an official statement from the company - but "leaking" on the Internet, although it might be protected under the law, can be seen by some as unethical.