Getting a list of all computer objects in each AD domain
One thing that I notice, you can change this repetitive fragment

if($($domain.DistinguishedName) -like "*DomainA*"){
    Write-Output ((Get-Date).ToString('MM-dd-yyyy:hh:mm:ss') + ": Moved $($comp.DistinguishedName) to $DomainAOUDump") | Out-File $log -Append
    Move-ADObject -Identity $comp.DistinguishedName -Server $($Domain.ReplicaDirectoryServers[0]) -TargetPath $DomainAOUDump 
}


Into the following (minus some variable definitions, e.g. $TimeStamp):

$DomainPrefix = Get-DomainPrefix $Domain
$TargetPath = Get-Variable -Name "Domain$($DomainPrefix)OUDump"

Write-Output "$TimeStamp: Moved $DistinguishedName to $TargetPath" | Out-File $log -Append
Move-ADObject -Identity $DistinguishedName -Server $Server -TargetPath $TargetPath


with Get-DomainPrefix defined to capture the first character after "Domain", e.g.

Function Get-DomainPrefix([String] $DomainName){
    $DomainName -match "Domain(?&lt;Prefix&gt;.)" | Out-Null
    $Matches.Prefix
}


So, the script will become (minus definition for necessary functions to hide the complexity)

foreach ($Domain in Get-Domains) {
    foreach ($Comp in (Get-ComputerArray -Domain $Domain)) {
        if ( ShouldBeMoved -Computer $Comp ) {
            $DomainPrefix = Get-DomainPrefix $Domain
            $TargetPath = Get-Variable -Name "Domain$($DomainPrefix)OUDump"
            $TimeStamp = Get-TimeStamp
            $CompName = $Comp.DistinguishedName
            $Server = Get-Server

            Write-Output "$TimeStamp: Moved $CompName to $TargetPath" | Out-File $log -Append
            Move-ADObject -Identity $CompName -Server $Server -TargetPath $TargetPath
        }
    }
}


Note that the else clause is not handled in the simplified script above.

For further cleaning, you can redefine how you store the $TargetPath into a more friendly structure so that we don't need to use Get-Variable. Perhaps a map from DomainPrefix to the TargetPath.

Note: I'm not familiar with ADObject and stuff, so the variable naming might be a little off.