I think your problem is here
[VBA]
Dim Period1, Period2, Period3 As String

[/VBA]
This is dimming only Period3 as string, the others are Dimmed as variant. Each item requires a specific "As" to Dim it to a type.
"Set" is used to set the variable to a Range etc. If you just require the value, omit the Set.
Try the following
[VBA]
Option Explicit
Sub TextBox()
Dim WbAgg As Workbook, WsAggChrt As Worksheet
Dim Period1 As String, Period2 As String, Period3 As String
Dim PPTApp As PowerPoint.Application
Dim PPTPres As PowerPoint.Presentation
Dim PPTSld As PowerPoint.Slide
Dim Sld As Slide
Dim TxtRng As TextRange
Dim foundText As TextRange
Dim ReplacePer1 As TextRange, ReplacePer2 As TextRange, ReplacePer3 As TextRange
Dim Shp
Set WbAgg = ThisWorkbook
Set WsAggChrt = WbAgg.Sheets("Chart Data")
Period1 = WsAggChrt.Range("M2")
Period2 = WsAggChrt.Range("M3")
Period3 = WsAggChrt.Range("M4")
Set PPTApp = GetObject(, "PowerPoint.Application")
Set PPTPres = PPTApp.ActivePresentation
PPTApp.ActiveWindow.ViewType = ppViewSlide
Set ReplacePer1 = PPTPres.Slides(147).Shapes(3).TextFrame.TextRange.Lines(2).Words(Start:=3, Length:=6)
Set ReplacePer2 = PPTPres.Slides(147).Shapes(3).TextFrame.TextRange.Lines(3).Words(Start:=3, Length:=6)
Set ReplacePer3 = PPTPres.Slides(150).Shapes(3).TextFrame.TextRange.Lines(2).Words(Start:=3, Length:=6)

'Automated Footer - 2004 Period Replacement
For Each Sld In PPTPres.Slides
For Each Shp In Sld.Shapes
If Shp.HasTextFrame Then
Set TxtRng = Shp.TextFrame.TextRange
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer1, Replacewhat:=Period1)
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer2, Replacewhat:=Period2)
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer3, Replacewhat:=Period3)
Do While Not (foundText Is Nothing)
Set TxtRng = TxtRng.Characters(foundText.Start + foundText.Length, TxtRng.Length)
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer1, Replacewhat:=Period1)
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer2, Replacewhat:=Period2)
Set foundText = TxtRng.Replace(FindWhat:=ReplacePer3, Replacewhat:=Period3)
Loop
End If
Next
Next
End Sub

[/VBA]