I was able to clear out most the errors, but the VMs keep connecting to the vApp network when deploying, not the organization network. The organization network is now getting created during deployment for use, but isn't being connected to. Here is what I have now:
Connect-CIServer -Server URL.com -User user -Password password -Org Demo-Area
$numVapp=2
$vappTemplate = Get-CIVappTemplate -Name "Centos_63_x64"
$myOrgNetwork = Get-OrgNetwork -Name "Demo-Area-Direct"
$vAppBaseName="scriptDB-"
for ($i=1; $i -le $numVapp; $i++){
New-CIVApp -Name ($vAppBaseName + $i) -VAppTemplate $vappTemplate
New-CIVAppNetwork -Direct -ParentOrgNetwork $myOrgNetwork -VApp ($vAppBaseName + $i)
Get-CIVApp -Name ($vAppBaseName + $i) | Get-CIVM | Get-CINetworkAdapter | Set-CINetworkAdapter -Connected $true -IPAddressAllocationMode Pool
}