Whenever you mess up with authentication methods on the IIS or through powershell, services may not function properly, especially the published ones. Blew is the default authentication methods published at Exchange Team Blog site:

Exchange Server 2010 with the Client Access Server (standalone):

Location

Authentication

SSL Setting

Management

Default Web Site

Anonymous

Required

IIS Management Console

aspnet_client

Anonymous

Required

IIS Management Console

Autodiscover

Anonymous / Basic / Windows Authentication

Required

Exchange Management Shell

ECP

Anonymous / Basic

Required

Exchange Management Console or Shell

EWS

Anonymous / Windows Authentication

Required

Exchange Management Shell

Microsoft-Server-ActiveSync

Basic

Required

Exchange Management Console or Shell

OWA

Basic

Required

Exchange Management Console or Shell

Powershell

Anonymous

Not Required

Exchange Management Shell

RPC

Basic / Windows Authentication

Required

Exchange Management Shell

RpcWithCert

all options Disabled

Required (128 bit not checked)

N/A

OAB

Windows Authentication

Not Required

Exchange Management Console or Shell

Exchange Server 2010 Mailbox role (standalone):

Location

Authentication

SSL Setting

Management

Default Web Site

Anonymous

Required

IIS Management Console

PowerShell

Anonymous

Not Required

Exchange Management Shell

CMDlet list for those that can only be modified in the Management Shell:

Set-AutoDiscoverVirtualDirectory

Set-WebServicesVirtualDirectory

Set-PowershellVirtualDirectory

Set-OutlookAnywhere (for the RPC virtual directory)