Yes.
Obviously, the more familiar with the whole buying & selling process you are, the more comfortable you will feel going to the notary without legal representation. Also your level of Spanish may make a difference. Sometimes it's worth paying someone just for translation purposes, for added confidence that everything is going correctly. The biggest concern, as you say, is making sure all the due funds come your way. Fortunately nowadays the black money thing is gradually disappearing; if you are receiving the entire proceeds above the table, so to speak, there will be none of that worrying about whether the buyer will hand over the rest of the dosh after the notary has left the room and after you have effectively signed your property over. If there is a portion of black involved, try to get it before signing, or at least ask the buyer to allow you to check it first.
Obviously (I think?!) you must get a bankers draft for the official amount of the sale, no personal cheques. Make sure you get a copia simple before leaving the notary, so that you have a copy of the details of the transaction.
Changing the electric and water contracts should be done by the buyer. If he doesn't get them put into his name, and as a result gets his services cut off, it's his problem. However, you won't want to keep receiving bills in your name for a property you have sold, so you may want to check that he will do it, or reach an agreement to do it together, for example. Bring copies of the most recent (paid) bills to the notary; with these and the copia simple, the buyer can do all the rest. Is there an agent involved? If so, get them to do all the running around - it's what they get paid (too much) for! You will need to get from the community administrator, and signed by the president, a letter stating that there are no outstanding fees due. There may be a small admin charge for this. Again, bring it with you to the notary (keep a copy!) Afterwards, let the administrator know the details of the new owner, and cancel any standing order you have to pay the fees. You also need to get a certificate from the rates department of your town hall, stating that there are no charges outstanding there. Probably need 24-48 notice for this. Bring it to the notary, keep a copy (you get the picture!) If you are resident in Spain, you must get a certificate from Hacienda proving that you pay your taxes etc. Otherwise, 3% of the declared sale price will be retained at the notary against potential CGT as if you are non-resident.
Finally, remember to bring your identification, and a bottle of water! I think that just about covers everything.
Sometime within 30 days (I think) of the sale, take your copia simples from when you bought and from the sale to the relevant office at your town hall to pay the plus valia tax. Unless you've owned the property donkeys years, this is unlikely to be too much.
Next year you may have a CGT liability, but that's for another day and another thread!