I read the OP and I see trouble. Here we have (I'm assuming) an entry-level worker digging into regulations and contemplating filing grievances over an occasional paycheck being one or two days late.
I've worked at a number of places where that wasn't uncommon, where you learned to cash the paycheck before depositing it to avoid it bouncing later and messing with your finances. Her complaint amounts to a very small inconvenience, and any attempt to force her boss to comply will not be received well.
What happens when she's applying for her next job and during a reference check her previous employer brings this little matter up?
If I were on the hiring committee (I'm on two currently) I see red flags. I see a person who's more concerned with the letter of the law, than the spirit. I see someone who gets lost in minor details and lets it potentially get in the way of her work and working relationships. I see someone who lacks perspective and the ability to roll with punches. I see someone that I'd be very leery about hiring.
Hm.
While I see what you are saying when you write this post, I do find myself wondering whether the somewhat varied reactions to this are yet another manifestation of the differences between attitudes to such things in the US and in Europe, and reflect the different relative strengths of the employer/employee relationship on the Two Respective Sides of the Pond.
This is because if salaries are late by a day or two in most European companies, - and international organisations - questions are asked, and the staff do tend to let their managers and employers know about this, and in no uncertain terms. Salaries are not a discretionary element of the employment contract in most cases, and nor are they an optional extra. They are expected and due, and other matters - say, for example, direct debits - are predicted on monies being there to meet them.
Now, as it happens, I have worked for international organisations where - again - on occasion, salaries were a little late arriving in bank accounts; it was the usual stuff, people on leave failing or forgetting to sign off on stuff, casual carelessness, failure of oversight and so on. However, those at the receiving end were not slow in expressing their displeasure, and invariably, management apologised profusely. And nobody would be penalised whatsoever for drawing attention to management incompetence or carelessness on such an issue.
So, I do see the OP's issue, here, and I would be a little concerned at the blithe disregard that many on the thread seem to express, arguing that this is 'not uncommon' and that it is a 'minor inconvenience'. Some people earn such low incomes that they have little choice but to live from cheque to cheque - (check to check?), meaning that, therefore, a delay of a few days may be a bit more than a minor inconvenience, especially if there are other demands for payment.
Indeed, if the actual delay is the fault of the boss, - although that is not clear from the OP's original post - I am not sure that a boss would use that very example during a reference check, as this is something that would not exactly reflect terribly well on them, either.
Having said that, as I advised in earlier posts, I would recommend holding my fire on this - especially if it is the first time it has happened, and seek to find out what exactly happened, and why it happened before even beginning to contemplate proceeding any further.