So, the problem is that you've got an array, and PowerShell doesn't know what you want done with it. I'm not sure how you're producing the HTML, but ConvertTo-HTML, as one example, can't "expand" an array for you. You'd need to do that yourself. I *suspect* that what you've got is an array of strings, which means you might try:
$admins = Invoke-Command -ComputerName $name -ScriptBlock {net localgroup "Administrators" | where{$_ -and $_ -notmatch "The command completed"} | select -skip 4} | Out-String
To turn the array into a flat string. Now, a potential problem is that it'll probably use carriage returns, which HTML won't render. I'm not sure if...
$admins -replace "\n\r","
"
Would work or not, but I'd try that, to convert the carriage return into HTML "line break" tags. I'd probably have to fuss with it along those lines until I got something like what I wanted.