This question from C:

Is there a setting/way to tell Outlook to run all client-only rules on inbox whenever the application is opened. This way when I come in Monday morning and open Outlook, everything will be filed/classified correctly.

Outlook will run all rules that are enabled when messages are downloaded, although, some rules can fail if there are a lot of messages to process (which is not uncommon when starting Outlook after a weekend away). You can use Outlook's Run Rules Now command to run the rules at any time, with Outlook 2010 and up adding a Select All button in the Run Rules Now dialog.

You can add the Run Rules Now command button to the ribbon or QAT for faster access to the dialog.

If you want something more automatic and are using Outlook 2007 and up, you can run rules using a macro. To run the macro automatically, call the macro from the Application Startup macro, or add it to a button on your ribbon to run it on demand.

Use a macro

Start with the macro from Outlookcode.com, which automates the process of using Run Rules Now, running all rules on the Inbox. As each rule runs, an Outlook dialog box shows you which rule is currently being processed. By adding rl.IsLocalRule = True to the If statement, you can run only the local, or client-side, rules.

At the end, a message box displays, letting you know that the macro is finished. This message box can be removed by deleting (or commenting out) each line that references rulelist.

If you need help using a macro, information and screenshots are at How to use the VBA Editor

Private Sub Application_Startup()
   RunAllInboxRules
End Sub

Sub RunAllInboxRules()
    Dim st As Outlook.Store
    Dim myRules As Outlook.Rules
    Dim rl As Outlook.Rule
    Dim count As Integer
    Dim ruleList As String
    'On Error Resume Next
     
    ' get default store (where rules live)
    Set st = Application.Session.DefaultStore
    ' get rules
    Set myRules = st.GetRules
     
    ' iterate all the rules
    For Each rl In myRules
        ' determine if it's an Inbox rule
              If rl.RuleType = olRuleReceive And rl.IsLocalRule = True Then
            ' if so, run it
            rl.Execute ShowProgress:=True
            count = count + 1
            ruleList = ruleList & vbCrLf & rl.Name
        End If
    Next
     
    ' tell the user what you did
    ruleList = "These rules were executed against the Inbox: " & vbCrLf & ruleList
    MsgBox ruleList, vbInformation, "Macro: RunAllInboxRules"
     
    Set rl = Nothing
    Set st = Nothing
    Set myRules = Nothing
End Sub