It depends how old you mean.The only disadvantages I can think of are that being an older parent would physically tire you out more, that you may be be a pensioner when your child is a teenager and going through that awkward rebellious stage.Also that your child may be embarrassed by having an older parent.
Apart from that,older parents are no different and may be better than young parents in that they are more patient and wiser. I was only 21 when my eldest was born and 33 when my youngest was born and I can definitely say that I think I am a better parent to my youngest than I was my eldest. I was too immature,selfish and impatient when I was 21.I do find my youngest a lot harder work though.I certainly wouldn't want to leave having a family any later than mid thirties, forty at the latest.Physically I don't think you're at your best past 40.