Overview:

As currently implemented, the "Book of Ancient Secrets" Eldritch Invocation incorrectly allows high level spell selection for multi-classed casters.

Relevant Rules:

The Book of Ancient Secrets feature reads "On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your *warlock* level (rounded up)"

Steps to Reproduce:

1. Create a Human Character with 13+ Cha and 13+ Dex that starts as Warlock 3
2. Select "Pact of the Tome" as Pact Boon and "Book of Ancient Secrets" as an Eldritch Invocation. 
3. Check the spells available to be transcribed under "Book of Ancient Secrets" and notice that only ritual spells up to level 2 are listed (correct implementation). 
4. Add 2 multi-class levels in Fighter. 
5. Check the spells available to be transcribed under "Book of Ancient Secrets" and notice that only ritual spells up to level 2 are listed (correct implementation). 
6. Add 2 multi-class levels in Sorcerer.
7. Check the spells available to be transcribed under "Book of Ancient Secrets" and notice that "Tiny Hut" and "Feign Death" (level 3 ritual spells) are now available for transcribing.

I could not reproduce this bug.

Can you link the affected character?

Here is an example: https://www.dndbeyond.com/profile/KenBrewer/characters/10158421

If you check the spells, you'll see that I have two level 3 ritual spells that have been added to my character sheet and supposedly can be cast. 

I just ran into this. 

Started with 4 levels of rogue, multiclassed into warlock, then some more levels of rogue. The ritual spell list after the first two now shows up to level 6 ritual spells. If you look at his spell list, you'll see Rary's Telepathic Bond is there, which is a level 5 spell. 

Linked character: ddb.ac/characters/21650449/sWMK7o

This might be answered somewhere else... but my theory is the extra slots appear so as you come across spells with the ritual tag and add them to your book, those slots let you add the spells to the invocation so they show up on your character sheet properly.

This should not still be a problem. When you select the Book of Ancient Secrets after gaining the Pact of the Tome as a 3rd level warlock you should be able to select rituals up to 2nd level.

If you later add other class levels, it does not affect the level of the spells you are able to select.

I made a Warlock 3 / Sorcerer 9 to test. This is what I see in the ritual drop down:

Edit: I screenshotted the wrong menu pick, but the bottom box (the one that lets you pick any level your WARLOCK levels can cast, was working correctly)

Quote from Houligan >>

This should not still be a problem. When you select the Book of Ancient Secrets after gaining the Pact of the Tome as a 3rd level warlock you should be able to select rituals up to 2nd level.

If you later add other class levels, it does not affect the level of the spells you are able to select.

I made a Warlock 3 / Sorcerer 9 to test. This is what I see in the ritual drop down:

 You're looking at the first dropdown. The first 2 dropdowns are for the 2 1st-level rituals that you get when you take the invocation. But I just tested with a massively-multiclassed test character with 3 levels of Warlock and it only sees 1st- & 2nd-level rituals as options in the third dropdown, so that's working correctly.