So I noticed that my wizard can learn cleric spells like false life and inflict wounds. Is this a bug?

+1

I refuse to learn them out of principle :P, though I might try for debugging reasons.

Yes, it's a bug, it will be fixed.

Should be a bug. But not sure

When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.
Only spells on the Wizard list can be learned in this way. Even if the game allowed you to copy a non-Wizard spell into your spellbook, we have in Preparing and Casting Spells, page 30 PHB

You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell). So even if you could write non-Wizard spells in your spellbook, you couldn't prepare them and therefore couldn't cast them.

Wizards can't use scrolls that are not on their list either, since we have on page 60 of the DM's Basic Rules:

If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible.

Ah, this makes me feel better. Hopefully it's correct. I started the game by making a warlock, which felt really fun and powerful until I learned that the wizard can essentially learn 100% of the same spells, except for eldritch blast. In the game's current state, I can't glean the advantage of having a warlock over a wizard. And if eldritch blast is really the only defining feature of a warlock, that's pretty disappointing.

As of right now, is there actually any advantage to choosing a warlock instead of wizard? To me it feels like a warlock is just a wizard with far fewer spells slots, and one different cantrip (eldritch blast).

As a seasoned 5E player I can tell you....eldritch blast + agonizing blast + hex kind of is the defining feature of a warlock.

They can do other things, but their 2 spells only per short rest really limits them. You cast hex and armor of agathys and that’s it.

You have to view warlocks more as a fighter or ranger that can cast some spells than as a full caster like a wizard. Most of the time you will be attacking with eldritch blast, just like a fighter would attack with their weapon.

Yeah noticed this as well. Defenitly a bug or at least unintended im sure!

I too noticed this. I also noticed that if you learn a scroll like for example Mage Armour, then as you level and you can pick new spells you can get Mage Armour again and it's not an option for the memorized when you are leveling. However outside of leveling and through the normal method to change out spells you can pick it there.