Based on Cann, Chapter 7, and my own knowledge.
BIG PICTURE ISSUE 1: bright-line rules v. balancing tests. Bright lines provide clear guidance to lower courts, administrators engaged in risk management (litigation avoidance) and lawyers. Balancing tests invest more discretion in administrators to innovate, but also give judges and lawyers more veto points in the administrative process. You can fight over which you think is normatively better; I don't really have a strong opinion.
BIG PICTURE ISSUE 2: sovereign immunity and ex parte Young. Basically, the state cannot be sued without its permission, which Congress can grant for the state (and that's an interesting federalism theory issue). The work-around for this is that you sue the office-holder personally. This creates a remedies issue, as the liability for some of these claims can be quite large, and liability can accrue even when you act in good faith. Almost every public employer will indemnify officials who are sued under the ex parte Young doctrine. My advice: don't work for a tiny town, because they're likely to leave you to twist (and they're also likely to have bad advice as to what they can and can't do).
So, the basic issues in considering the law of public employment are "who can sue you, as an administrator, and why?" and "who can you sue, as an employee, and why?" So, taking these in reverse order:
Employment litigation by public employees: This falls into three categories: procedural due process, substantive due process, and equal protection. Due process claims arise when a life, liberty, or property interest is implicated; no one can argue with any seriousness that these claims implicate the interest to life, so you're left with liberty interests and property interests.
Property interests create procedural due process claims. These are the easiest to prove, if you can get to trial; but they're difficult to get to trial. Why? Because very few public employees have a property interest in their job, particularly now as the state dismantles civil service protections and public-employee collective bargaining; because it's not terribly difficult for the public employer to provide appropriate due process if you do have a property interest. Frankly, my experience in litigating these types of claims is that the usual fight is over whether the employee had a property interest in their job. So these cases resolve after summary judgment, usually; if the employee is found to have a property interest in their job, the case settles for a fairly significant amount; if not, then they settle for what I call "shut-up money." So procedural due process claims are more interesting from the litigation avoidance perspective.
How can you tell if the employee has a property right in their job, and thus is entitled to procedural due process? 1) Do they have a contract of employment? If not, then they have no property right. Be careful that the employee handbook doesn't accidentally create a contract (also consider the possibility of promissory estoppel). 2) If they have a contract (either individual or through collective bargaining), then look at the terms of the contract. Does it limit termination to "for just cause or financial exigency?" Then there is a property right. Does it provide for an internal grievance procedure or arbitration? That may, sometimes, be interpreted as creating an expectation sufficient to create a property right. Does it contain some sort of clause allowing management to exercise the prerogatives of management, including hiring and firing? Then probably not creating a property right. Is it for a fixed period of time? Then definitely there is a property right, although it may be less protective than "just cause" provisions.
Employers can avoid these types of claims by providing procedural due process to all employees, regardless of their status - but that can be burdensome, even if it's not difficult. After all, what does due process require? Prior to termination, the employee must be given a hearing, which need not be particularly onerous, but can be as elaborate as the employer wants. The employee must receive "sufficient" notice, which means who knows what; an explanation of the evidence against them; and an opportunity to present their side of the story. Sometimes this actually demonstrates a mistake, and the termination is not done. More usually, it's basically just a hoop the employer has to jump through before you're gone. Post-termination, you have to get a more extensive hearing, although what that hearing has to entail is not always clear. It seems like it needs to be more formal; you and the employer have to be on equal footing (i.e., if you don't have a lawyer, they shouldn't use one either); and the decisionmaker needs to be neutral. This last can be problematic in getting rid of top administrators like school superintendents, where the decisionmaker (the school board) is usually also the supervisor who wanted to fire the administrator to begin with. Ask me about Pine Bluff, Arkansas to talk about that. For adverse employment actions short of termination, we see a balancing test that asks the court to weigh the private interest in continuing the status quo ante against the public interest in the new status quo.
Liberty interests create substantive due process claims. Here's the problem: should the government be held to the same standard for substantive due process claims when it acts like an employer as it is held to when it acts like a sovereign? The Court says no. What's the argument for that approach? Just as there is no constitutional right to expectation in employment, employers generally have the right to police your speech and action within the course and scope of your employment. It does not make sense to the Court that the employer suddenly loses this right just because the employer is a government agency. Thus, your public employer has the right to control how you act and speak on the job. Thus, the question becomes when you are "on the job" for the purposes of speech, right? This gets into the Pickering/Connick/Garcetti test (or the National Treasury Employees test, but that one's is more about issues of pay-for-play in government). Briefly: you are protected from adverse employment actions based on your exercise of constitutional rights when you a) act on a matter of public concern; b) as a citizen; and c) not as a requirement of your public employment. See my GMUCRLJ article for 14K words more on that.
Discrimination claims: Cann is not quite right when he talks about this issue. He says that public employers are covered by Title VII and FMLA, which is true, and he does not mention ADEA and ADA, which is because the Court held that Congress had not abrogated sovereign immunity in those statutes. BUT, there is a work-around. Using the ex parte Young doctrine and suing under 42 U.S.C. 1983, you may be able to argue age discrimination or disability discrimination even without the abrogation of sovereign immunity. There are circuit splits on both issues, and the Supreme Court granted certiorari, then dismissed it as improvidently granted post-oral argument on the ADEA issue last year. Other employment statutes you need to be aware of as an administrator, both as a potential plaintiff, and as a supervisor who may violate one of them: FLSA (all employers covered); USERRA (no solid answer on state employers, but federal covered); GINA (same scope as Title VII). Ask me after class if you're interested in cutting-edge theories of liability that may apply to you in your public employment.
N.B.: ALL of these types of claims are subject to additional penalties for retaliation.
Suits against administrators by constituents: These basically boil down into procedural due process claims (which are analyzed similarly to the PDP claims by employees, but can also, particular in the prison context, implicate liberty interests); substantive due process claims (which are analyzed very differently to SDP claims by employees, and are beyond the scope of this presentation); and equal protection claims (which are analyzed according to the classification being alleged, and that is also beyond the scope of this presentation). All three of these claims, and any other claims that are not specifically authorized by legislation, are brought under 42 U.S.C. 1983 under ex parte Young. If there are types of claims specifically authorized by legislation, then that statute will explain both how they are brought and what remedies are available.
State law: Varies from state to state. Good luck.