I have always ordered my certs from the local record office (superintendant registrar), and have to date had no problems. Some take longer than others, but this is dependent of the number of staff. The one I use most only works mornings 4 days a week, so it does take a bit longer.
Before I order, I always phone first to check cost etc. Some offices ask for an SAE which is a problem for me, living in Germany. Some of them then ask for an additional 50 p or whatever to cover postage. Others just laugh and say its OK. I haven't ordered on line as yet, as I find the personal touch brings significant advantages with it. I only pay 7 pounds!
The advantage with the personal touch is that once they get to know you, they will be more willing to do a few extras, extend a search a bit etc. So long as you don't abuse it.
When ordering certificates, I provide all the info I have pertaining to the application, incl. parents names, or childrens names if its a death cert. By doing this, and adding a qualifying statement such as on a marriage cert "if the brides father is not called such and such, I do not require the certificate." I have to date not received any wrong certs. Granted this is not so easy if parents a siblings names are not known.