Once someone becomes an executor, she has all the authority she needs to settle the deceased's estate. The executor can pay taxes, pay debts, write checks, and sell off assets to pay the deceased's tax bills. Beneficiaries do have rights during this process, but the executor doesn't need them to sign off on her actions.
An executor usually gets the job because the deceased named her in the will. That doesn't give her authority in itself: The executor has to file with the probate court to confirm her position. The court then provides letters testamentary, which prove to banks, investment firms and attorneys that the executor is the real deal and not trying to defraud the estate. Those letters and her own signature are all the authority an executor requires to sell assets or settle debts.
If a beneficiary objects to the choice of executor, he has the right to file objections with the court before the judge issues the letters. He's entitled to know what the estate's assets are and to stay informed about the estate accounts. That includes the right to go over invoices, receipts, cancelled checks and other key documents. If the executor doesn't provide information about the estate when asked, the beneficiary can request that the probate court supervise a review of the accounts.
If the beneficiary co-owns some of the deceased's assets, things get more complicated. Co-ownership with a right of survivorship bypasses probate completely: The beneficiary, having survived the deceased, gets full ownership automatically. Without a right of survivorship, the beneficiary retains part ownership, but the rest belongs to the estate. The executor can sell the estate's share of the property, but she can't sell the entire asset without the beneficiary's approval.
If the beneficiary decides the executor is mismanaging the estate and selling assets that need not be sold -- or worse, selling them to line her own pockets -- he can ask the probate court to remove the executor. The court is unlikely to act if it's only a matter of judgment: The errors must be serious. If the court removes the executor, it will appoint either an alternate executor named in the will or use state law to select one.