Is it right for the pastor to have authority over the finances?
The pastor may have some involvement or authority in the church finances. However, for the protection of his reputation and the church's resources, there should always be good segregation of duties. The pastor should not have sole access to cash receipts or disbursements.
Related to cash receipts, two people should count money that is received and sign off on the deposit slip. It would be best if the person entering information into the donor system was not the individual making the bank deposit. This allows for a reconciliation of the money deposited to the donor records and finally the system is verified when donor receipts are issued.
Cash disbursements steps should be segregated between people processing information in the accounting software and check signers. An individual with access to the accounting records could "cover their tracks" if they were a check signer that made improper payments. The same separation of roles is important for the payroll process so that an individual cannot pay individuals inappropriately.