0x80070002 when adding web part using Powershell

I was adding a webpart using this powershell:
$webpart = New-Object Microsoft.SharePoint.WebPartPages.SilverlightWebPart
$wpm = $web.GetLimitedWebPartManager($page.Uri.OriginalString, "Shared")
$wpm.AddWebPart($webpart, 'Header', 0)

... and got this error:

Exception calling "AddWebPart" with "3" argument(s): "<nativehr>0x80070002</nativehr><nativestack></nativestack>"
At line:1 char:16
+ $wpm.AddWebPart <<<< ($webpart, 'Header', 0)
    + CategoryInfo          : NotSpecified: (:) [], MethodInvocationException
    + FullyQualifiedErrorId : DotNetMethodException


It turns out that my $page was the wrong one which was not checked out nor editable at the time.

Listing a page's web part zones

I have been trying to figure out a way to list all of a page's web part zones. There is not much documentation out there on this. Here's what I have been able to figure out. It is for a publishing web, but the procedure should be pretty much the same.

$myweburl
$mylayouttitle
$web = Get-SPWeb $myweburl
$pWeb = [Microsoft.SharePoint.Publishing.PublishingWeb]::GetPublishingWeb($web)
$layout = $pWeb.GetAvailablePageLayouts() | Where-Object {$_.Title -eq $mylayouttitle}
$layout.ListItem.Properties['vti_cachedzones']


And to list the webparts on a page:
$pageurl
$wpm = $web.GetLimitedWebPartManager($pageurl, 'Shared'
$wpm.WebParts | Format-Table -AutoSize WebBrowsableObject, ZoneId, ZoneIndex


There's also a post Determine which webpartzones are on a webpartpage that uses reflection to get at a private member however I have not gotten it to work.

Locking down web part zones

One use case in my SharePoint demo environment is to show that certain web part pages have mandatory web parts while others can be customized by the end user. The way to accomplish this is to put the web parts in different zones. Then add the following properties to the <WebPartPages:WebPartZone> element: AllowCustomization="False" AllowPersonalization="False" AllowLayoutChange="False"
Simple! Or you could do this using SharePoint Designer.