SharePoint 2010, Powershell - Loop through all Document Libraries, create view and set it as default - sharepoint

Question

I'm having a little trouble with a script I'm working on for SharePoint 2010. I'm only a beginner with Powershell so haven't been able to to spot the no doubt obvious and glaring problem.
The desire for the script is to loop through each web-site in each site collection, create a view for Document Libraries only and set that view as default.
Issue 1) Currently it appears to enumerate the Document Libraries but then creates the view multiple times in the first library it found. Something is wrong with the foreach loops but I don't know what.
Issue 2) I need to integrate this section so I can set the view as default but I'm not too sure where to stick it so it loops through with the changes to each library.
$site= New-Object Microsoft.SharePoint.SPSite $siteURL
$web=$site.OpenWeb()
$list=$web.Lists["$list"]
$view=$list.Views["Detailed"]
$view.DefaultView = $true
$view.Update()
$list.Update()
Any assistance on these two issues would be of great help:-). Thanks, Ashley
Full Script:
Add-PSSnapin Microsoft.SharePoint.PowerShell -erroraction SilentlyContinue
$siteURL = "http://sp14fdev01/"
$site = Get-SPSite($siteURL)
foreach($web in $site.AllWebs) {
foreach($list in $web.Lists) {
if($list.BaseType -eq "DocumentLibrary") {
$site = New-Object Microsoft.SharePoint.SPSite($SiteURL) ;
$web = $site.OpenWeb($SiteURL);
$list = $web.Lists.item($listname);
$viewfields = New-Object System.Collections.Specialized.StringCollection
$viewfields.Add("DocIcon")
$viewfields.Add("LinkFilename")
$viewfields.Add("_UIVersionString")
$viewfields.Add("FileSizeDisplay")
$viewfields.Add("Created")
$viewfields.Add("Modified")
$viewfields.Add("Editor")
[void]$list.Views.Add("Detailed", $viewfields, "", 100, $true, $true)
$list.Update();
}}
$web.Dispose();
$site.Dispose();
}

Answer 1

The changes are explained in the comments.
Add-PSSnapin Microsoft.SharePoint.PowerShell -erroraction SilentlyContinue
$siteURL = "http://sp14fdev01/"
$site = Get-SPSite($siteURL)
foreach($web in $site.AllWebs) {
foreach($list in $web.Lists) {
if($list.BaseType -eq "DocumentLibrary") {
// the variables `$web` and `$list` already reference the objects you need
//$site = New-Object Microsoft.SharePoint.SPSite($SiteURL) ;
//$web = $site.OpenWeb($SiteURL);
// new instance of the list is necessary to avoid the error "Collection was modified"
$newList = $web.Lists.item($list.ID);
$viewfields = New-Object System.Collections.Specialized.StringCollection
$viewfields.Add("DocIcon")
$viewfields.Add("LinkFilename")
$viewfields.Add("_UIVersionString")
$viewfields.Add("FileSizeDisplay")
$viewfields.Add("Created")
$viewfields.Add("Modified")
$viewfields.Add("Editor")
[void]$newList.Views.Add("Detailed", $viewfields, "", 100, $true, $true)
$newList.Update();
// setting the default view
$view=$newList.Views["Detailed"]
$view.DefaultView = $true
$view.Update()
}
}
$web.Dispose();
}
$site.Dispose();