See subject of positing for question.
1) I recall seeing a really cool option in VB.NET using LINQ to match using "LIKE%'
2) I know regular expressions will work and I suspect that will result in the shortest code and probably won't be too hard to read for such a simple test.
Here's what I did. Warning: You're gonna hate it.
Private Shared Function FileNameIsOk(ByVal fileName As String) As Boolean
For Position As Integer = 0 To fileName.Length - 1
Dim Character As String = fileName.Substring(Position, 1).ToUpper
Dim AsciiCharacter As Integer = Asc(Character)
Select Case True
Case Character = "_" 'allow _
Case Character = "." 'allow .
Case AsciiCharacter >= Asc("A") And AsciiCharacter <= Asc("A") 'Allow alphas
Case AsciiCharacter >= Asc("0") AndAlso AsciiCharacter <= Asc("9") 'allow digits
Case Else 'otherwise, invalid character
Return False
End Select
Next
Return True
End Function