Exception calling "Update" with "0" argument(s): "The file
LibraryName/folder/test.docx has been modified by
i:0#.w|domainuser on 29 Mar 2017 17:41:05 +0100."
At C:ScriptsCheckout-UpdateCol-CheckIn.ps1:19 char:13
+             $item.Update();
+             ~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [], MethodInvocationException
    + FullyQualifiedErrorId : SPException

Add-PSSnapin Microsoft.SharePoint.Powershell
$SPWeb = Get-SPWeb "https://domain/sites/site"
$LibraryName = "Library Name"
$Library = $SPWeb.Lists.TryGetList($LibraryName)
$items = $Library.Items

foreach($item in $items)
{
    $itemDoc = $item.File
    if ($itemDoc.CheckOutStatus -ne "None")
    {
        $itemDoc.CheckIn("1 - checked in by script")
        if ($itemDoc.CheckOutStatus -eq "None")
        {
            $itemDoc.CheckOut()
            $item["Title"] = $item["New Title"]
            $item.Update();
            $itemDoc.CheckIn("2 - checked in by script")
        }
    }
    else
    {
        $itemDoc.CheckOut()
        $item["Title"] = $item["New Title"]
        $item.Update()
        $itemDoc.CheckIn("3 - checked in by script")
    }
}
$SPWeb.Dispose()