Hard to know without actually seeing the draft contract and knowing what the job spec is. So some things that typically need modification are:
Duties - remove babysitting from it. They are a nanny not a babysitter. If you want them to babysit that's fine to ask them on each occasion but don't have it in the contract.
Gross Salary (Section 2.1 of the Nannyjob version does state Gross)
Adjust payment method to what you are happy with. I would advise ditching every payment method except direct bank transfer.
Note: you should make sure the money is in your nannies bank account by the last working day of the month. Don't pay on that day... pay several days before hand so the payment has time to transfer/clear. Some banks will transfer instantly, others take a while.
Childcare Vouchers - are you using those at all? If so you don't need to put anything in the contract about it but you should make sure they clear in sufficient time. Suggest putting them in around the middle of the month, they can sometimes take ages to be paid. Payslips should ideally state how much money is paid via voucher and how much via bank transfer - you may need to write this onto a payslip if it's produced by a payroll company as the payroll company won't know about the vouchers.
2.4 The Nanny shall be reimbursed by the Employer for all reasonable expenses incurred by her in the performance of her duties under this contract, provided that the expenses are incurred with the approval of the Employer and provided the Nanny produces such evidence of expenditure as the Employer may reasonably require. Petrol costs will be reimbursed at the rate recommended by the Automobile Association if the Nanny uses her own car during performance of her duties.
I would change 2.4 so that it fits better with what you would actually be doing in reality. How are you deciding to operate a kitty - getting a receipt for every small thing can be tricky. You are trusting your nanny to care for your children, so trust them to operate a weekly kitty. If you get concerned about expenditure you could always ask them to keep a record for a bit to see what is costing more than is desirable. Also, do you want to approve each and every spend? Possibly not, I expect you want your nanny to be sensible.
Max travel reimbursement cost is shown on HMRC website - Approved Mileage Rates note that it changes after first 10,000 miles in the tax year.
As you nanny is using their own car... consider what is happening about child seats - whose responsibility to buy those? Car Insurance must also be suitable... Morton Michel provide a policy suitable for nannies. Other insurers may provide Class 1 Business, though may not specifically cover your children. Hard to know what is best to do car insurance wise as until a major claim is made you don't know how good the cover is. I don't think you can insist that your nanny has a certain type of policy, though you should make sure they discuss the situation with their insurer so their insurer knows they are being paid (at Approved Mileage Rate) to transport children.
Holiday Entitlement - make sure this is as clear as possible, especially about working/not working public/bank holidays.
6.3 Gross Misconduct - write out specifically what you consider gross misconduct to be. I advise using bullet points. Consider things the nanny might do whilst caring for your children... smoking for example.
Insurance for You... you need Employers Liability Insurance. This is usually part of your home contents policy (though Co-Op Insurance don't seem to include it). So check your policy, call your insurer if necessary.
We are sharing her tax code with another family, so do you advise I put the gross monthly wage in there?
Yes as the tax code could change and probably will change come April 2012. You can't predict the future, something could happen which means the nanny has additional deductions from salary at source.
With a gross salary defined it does not matter what happens to that taxcode, your cost remains the same being Gross salary + Employers NI.