Thought #1: Government employees have precisely zero reasonable expectation of privacy in the performance of their duties. The working areas of the White House should be completely covered by 24/7 live-streaming cameras with mics so that the people the White House claims to work for can monitor their activities at will. Yes, that should include the Oval Office. In the absence of that, no, I don't see any problem with Omarosa Manigault Newman keeping a digital recorder on her person and recording anything she considers important, relevant, or otherwise useful.
Thought #2: While I disagree with the whole idea of "classified information" for reasons that Thought #1 should make obvious, if such a system is going to exist, security clearances should be automatically revoked when those holding them leave government employment. Per the system, they no longer have any "need to know" classified information.
One of the justifications for someone like John Brennan keeping a security clearance after leaving government employment is that it's convenient in case some successor wants to consult him and get his advice. That's risible. Does anyone really believe that the Safety of the Republic depends on John Brennan, or any other individual, offering an opinion on an issue based on current access to classified information? Brennan keeping his security clearance isn't for the benefit of the government, it's for the benefit of Brennan. Its sole present purpose is letting his new employers -- NBC/MSNBC -- tout him to their audience as a Very Important and Unusually Well Informed Person.
One objection to Manigault Newman's recording of her firing by White House chief of staff John Kelly is that she brought a recording device into the Situation Room. My question is: Why the hell would Kelly take her to the Situation Room to fire her? The Situation Room is the venue in which highly sensitive matters of national security (that presumably couldn't be discussed in a White House with that 24/7 streaming I mention above) are supposedly discussed. The objection here should be that Kelly abused the Situation Room by using it to conceal stuff that was not classified, not that Omarosa exposed him for doing so. It's kind of like the DNC email dump in miniature: "Waaaah, shame on you for outing us, not shame on us for doing what we did!"
As for the notion of "nondisclosure agreements" for government employees: Not only no but f*ck no. According to the prevailing mythology they are OUR employees; Donald Trump is just someone we've hired to oversee them. If a shift manager at McDonald's got caught trying to make the cashiers sign agreements not to disclose stuff to the corporation's CEO, that manager's ass would be canned post-haste, and rightfully so.