How does the blockchain resolve arbitration issues? I understand that a bitcoin wallet is nothing but a transaction record performed on the block chain.
How are transaction details updated in the decentralised block chain?
In a centralised system a transaction is based on the transaction record maintained in their centralised servers. For example A and B are connected to centralised C. When   A initiates a transaction with B, C refers to its centralised database and verifies whether it is a valid transaction and permits the transaction based on the validation results. In other words, there is a central log for cross verification and debugging to settle issues when there is arbitration needed by any one of the two transacting parties.
But in decentralised transaction there is no centralised arbitrator. How is arbitration provided in case of a misplaced transaction?
In other words is there any confiscate mechanism to strip the owner of his bitcoins who is involve in illegal practices?
I understand that bitcoin wallet is nothing but transaction record performed on block chain.

A bitcoin wallet stores keypairs, and allows the use to interact with the network by sending/receiving bitcoin transactions.

How are transaction details updated in decentralised block chain?

A 'full node' can be run by a user that wants to independently verify the state of the network for themselves. Each full node keeps their own local copy of the network state (blockchain history), and the nodes communicate new blocks and transactions to each other. By doing so, all of the nodes will come to agree upon the current network state, without the need for a central server.

How are arbitration resolved in case misplaced transaction.

Network nodes follow a set of rules (often called 'consensus rules'), that allow them all to arrive at the same conclusion about what the network state should be. In the event of conflicting blocks, the chain with the 'most work' is eventually ruled the valid chain.

In other words is there any confiscate mechanism to strip the owner of his bit coins who involve in illegal practices?

No.