Use inserted to place x exactly once

Procedure SortedListInsert(L, x):
    newList = []
    inserted = false
    foreach z in L:
        if NOT inserted:
            if x < z:
                newList = newList ++ [x]
                inserted = true
        newList = newList ++ [z]
    if NOT inserted:
        newList = newList ++ [x]
    return newList

The flag remembers an event across loop iterations. Before insertion, test where x belongs. After insertion, stop testing x against new elements and just copy the remaining sequence. The line copying z is OUTSIDE the insertion IF, so every old element survives.

Use a new false flag for every procedure call. A true flag carried over from an earlier call would prevent insertion. The flag is a Boolean, the output is a list and x is an element; confusing these types changes the procedure.