How do the issues of due process and just cause affect employers' disciplinary actions?

How due process and just cause have an impact on the discipline of employees is mostly a matter of context and a matter of perception.  There is no one definitive answer to this question, so I will address a few different contexts for you.

First, if there is a collective bargaining agreement, it is quite likely that due process and just cause will be built into that agreement, such that grievances can be filed over disciplinary actions and an employer is required to have just cause for any disciplinary action. I have never seen a collective bargaining agreement in which these were not present.

Second, absent a collective bargaining agreement, if there is an employment contract of any sort, these may or may not be part of that contract. Employee contracts can contain a myriad of provisions, some allowing termination without due process or just cause, while others might contain provisions for one, the other, or both.

Third, to what degree any of this matters is largely a function of what state has jurisdiction over the situation. Some states are called "at will" states, which means that employees, absent some sort of contract, can be fired for no reason at all, as long as it is not for an unlawful reason, for example, race discrimination or pregnancy.  A few states have some worker protection built in, although I am not aware of any state that guarantees workers due process.

Fourth, it is quite important to understand that due process is guaranteed to us by government. There is no guarantee of due process in a private employment situation. That is simply not an entitlement of the American worker, unless that person is working for the government. 

Fifth, similarly, just cause is not an entitlement.  It is not an entitlement under the Constitution nor an entitlement in private employment. It is something that is valued by employees, but that by no means makes it a requirement.

Finally, in spite of the fact that they have no entitlement, employees who perceive disciplinary actions to be lacking in due process and just cause are likely to become disaffected employees very quickly, as will any workmates who have this perception, too.  Without either, we perceive the workplace to be quite unfair, and this is very bad for motivation and productivity. A wise employer will build in at least a modicum of due process and not act without good cause, lest the perception of unfairness permeate the workplace to the employer's detriment. 

So, it is important to consider collective bargaining agreements, other contracts, and what state has jurisdiction over the matter.  It is important to remember that absent a contract of some sort, neither is an entitlement.  Nevertheless, the perception of fairness is an important part of effective management, and some due process should be built in to discipline, and no disciplinary action should be occurring arbitrarily.