A better way might be to write the values to an array, or even to a text object. Arrays will work the fastest, but text might be best in this case because you can search for the items you want to remove. So if you're using a recent version of Vanilla, [text search] and [text delete] are probably your best bet. You can then use [text set] to add items and [text get] to retrieve them (in place of your [list-nth]).

Looking at your patch, I would also guess that part of the problem has to do with order of operations. The [o] right after the metro and the [arp] sub-patch both have two connections coming out of the outlets, but which one gets sent first? The patch won't work if you get the order wrong. Use [trigger] to define the order, and you might find that you've fixed the problem.

In case it's useful to you:
The idea of linked lists is that you would have 2 arrays -
1 storing the note values
1 storing a pointer to the next value to be played

for example if your arrays are
NOTE and POINTER
when the player presses C you might store
60 in NOTE (0) & 0 in POINTER(0).
if the player adds E then you would store:
64 NOTE(1) & 0 in POINTER (1) & 1 in POINTER(0)

so each time the player adds the nth note to the arpeggio, you store the note in NOTE (n) and you store a 0 in POINTER (n), and you store n in POINTER (n-1)

If the player releases a key then you just have to update the POINTER array so that the value BEFORE the released key now points to the value AFTER the released key. you don't have to bother tidying up the NOTE array until all keys have been released.
So you would search for a member of NOTE that matches the released key.
if you call that the nth member, then all you have to do is set POINTER(n-1) to the same value as POINTER(n).

This would also definitely be a useful technique if you wanted to do an up/down arpeggiator where the player can add and remove notes.

Now I'm scratching my head over, how to achieve the up/down mode of the arpeggiator. Any Tipps on that? Do I need another array for the notes, so that they are read from the nore array, that's already there, sortet and written into a new array? No, seems not very elegant to me...