If I have more than one address in a wallet; is there anything that links them other than wallet file?
In other words, can these addresses be tied together by someone else?
Not quite sure what you mean by “tied” together. But with a little bit of programming, you can “tie” them together in another place to monitor the transactions only by another person but not to transact as the other person won’t have your private keys to transact.
See this example here: http://blockexplore.in/search/richlist/
The richlist was “tied” together and the balances are shown via some programming.
No, i can’t think of anything.
What I mean is :
If I have a wallet with several addresses, can anyone determine that these addresses are all owned by myself?
Just for privacy, would this be a reason to make a separate wallet?
Nope. Each address is as anonymous as another wallet’s.
The reason to make another wallet is more likely if you don’t want to lose all the accounts in the wallet or if you want to organise them into folders, something I proposed much earlier, but was said as not practical. I still think it is a very practical way to organise accounts.
OK thanks !
I seem to recall (don’t know if it was NXT’s or another) blockchain explorer with addresses linked to each other as probably owned by the same user or something.
A little privacy may become necessary if NEM takes off 
You can prob do some analysis to take some guesses. For example always the same IP broadcasting txs from those accounts could suggest one and the same owner. I guess that’s very weak evidence though as you prob can’t know if that’s just a node passing them on or actually the initial broadcast.
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As Pat said a forensics expert that had been recording all data being trafficked through the network and then analyzing it could infer connections, and probably with a high degree of accuracy if those accounts were very active.
If they weren’t active and/or a person was paranoid and covered their tracks, it would start to become really difficult really quick.
No issue then…
I’m far from paranoid 
I just believe not everyone should know what I do with my money.
I think we pretty much all agree on that.