Your `insert` was too complicated for me to understand so I rewrote the code to:
proc push*[T](list: var LinkedList[T], val: T) =
## Appends a node with the given `val` to `list`.
#list.insert list.last, nil, val
var node = ListNode[T](val: val)
node.prev = list.last
# node.next remains nil
list.last = node
if list.first.isNil: list.first = node
proc unshift*[T](list: var LinkedList[T], val: T) =
## Prepends a node with the given `val` to `list`.
#list.insert nil, list.first, val
var node = ListNode[T](val: val)
node.next = list.first
# node.prev remains nil
list.first = node
if list.last.isNil: list.last = node
Run
And the errors that valgrind showed disappeared.
