In Waterdeep: Dragon Heist, there is an encounter that requires a large number of similar NPCs/monsters, based on the (slightly edited for spoilers) text block:

the City Guard arrives and cordons off the Alley, posting six guards at each entrance. The guards don’t allow anyone in or out without permission from a superior officer. Another six guards, including a sergeant with 18 hit points, make their way to the crime scene and watch over the scene until the City Watch arrives.

The stat block for guard has a single action as a spear.

However, presumably a squad of this size would have a mixture of weapons for different situations, ranges, damage types. So instead of 12 City Guards armed with spears, I have 4 armed with spears, 4 with maces and 4 with shortswords and changed the to hit modifier and damage to match the RAW attack and damage values for Guard, so if any combat starts, there should be no statistical difference (apart from vulnerability/resistance/immunity damage types).

Are there any unforeseen issues with changing the weapons like this? Are there better/recommended ways to make these changes?

Are there any unforeseen issues with changing the weapons like this?

Yes

The unforeseen issue is that you create the impression in the minds of the players that Waterdeep guards are an ad-hoc militia rather than an organized, standing force.

Efficient and effective state-run military/police have standardised equipment - uniforms, armour, ancillary equipment and weapons. Para-military militias have whatever they turned up with. Waterdeep guards are the former - you run the risk of making them look like the latter.

There is nothing wrong with them carrying spears and maces and daggers and choosing the appropriate weapon for the task at hand but they should all be uniformly armed.

Basically, Waterdeep guards look like this:

Not this:

As an aside, the overwhelming majority of weapons ever used in the pre-firearm age were spears for the obvious reasons: they're cheap, can be made by anyone (a basic spear is a stick with a point) and all the nasty stuff happens 6 to 12 feet away from the guy holding it.

The issue is that it will complicate play.

The only issue is that it is yet another thing to keep track of in the event they are in a battle. If you are willing to do the extra work required to keep yet another thing straight then it should be fine, but it will complicate things.

Organized militaries frequently used a variety of weapons together

I must respectfully disagree with Dale M's suggestion that it would make their unit disorganized. In parades the equipment was ruthlessly standardized, or at least similarly equipped troops are grouped together. In battle, it was more complicated. Organized units usually had the organizer provide their equipment, but that does not mean the equipment was always identical.

In the modern day, it is hardly uncommon to see a single infantry squad that has soldiers equipped with M16s while some have SAWs and some have M16s with grenade launchers. And that may be the standard equipment. They may also have one or two soldiers equipped with specialized gear for the the mission at hand.

Phalanxes often had standardized equipment inside the phalanx, but the phalanx itself was frequently supported by light-infantry acting as skirmishers, cavalry, archers, and possible slingers.

A fantasy setting would likely have even more diversity as there was more diversity in both the available weapons and the threats to be faced.

The DMG specifically mentions switching weapons as one option for modifying monsters (in the Creating a Monster section, p273-274). Since the weapons you're swapping in for the spears do the same damage, there's very little that needs changing for your sword-guard and mace-guards (just remove the text about wielding a spear in two hands from the statblock of the guards without versatile weapons).

The only "balance issue" you might run into (if you can call it that) is that shortswords and maces are worth a little bit more than spears. Neither swords or maces are expensive but spears are really cheap. If your party is very poor and they have the time to loot the guards after killing them, you may be giving them a little bit more value than you intend (though you might make the difference up later by making it very hard to sell the "stolen" weapons in the city). It's not going to be difference though, and if ~50 gp in loot swings the balance of your game, you probably have other problems. If your players are sufficiently well equipped, they don't care about a bunch of mundane weapons, so you can probably ignore the weapon values completely (or, you know, prevent them from having enough time to loot).

But it does bring your assumption about the guards' armaments in to question. You say that they should have a diversity of weapons to fight diverse threats. But that may not be the guard's purpose. Mostly they're there to tell city residents they can't come in or out of the alley rather than to fight, and for that any weapon may be as good as any other. It may be more likely that the city guard is equipped as inexpensively as possible. Giving them all spears is cheaper for the city than giving them a mix of weapons, and it also simplifies training and administration.

So I say: Feel free to change a creature's equipment if you want to. The DMG even tells you it's a good way to customize monsters. But also feel free not to bother, if the new gear doesn't make a significant difference. Or make it serve some other purpose, like making some individual guard stand out. If a squad of six guards has five guys with spears and one with a shortsword, your players may think the one guy with the sword is special somehow. Perhaps that's a subtle way to distinguish the sergeant from the rest. Or maybe it's a red herring!

I think changing the weapons makes sense.

A city guard is not a soldier. In battle (especially if it's a phalanx) identical equipment makes sense. But guards have various tasks, they were the police of the time.

Imagine that you're a guard investigating something, so you go into a house. Or the house's cellar where someone is supposedly hiding. You wouldn't bring a long weapon there, would you? In the street on the other hand, you won't try to stop a horseman with a dagger either. Despite this, sometimes you need to be armed, and you can't have both if the cost is high. So some guards (let's say the officers) have shorter weapons, while others stay outside with spears.

By the way, Matt Easton, Lindybeige, and a few volunteers tested the spear, and it performed very well. If your guards can afford to have both a spear and a shorter weapon (for close quarters combat), choosing both makes sense. Also, mixing in archers/crossbowmen to cover them adds some challenge.

In this specific game replacing some of the spears with different equipment is perfectly acceptable.