Hi Missty,
1. Your poolman should check not only chlorine but also acidity levels every week and adjust accordingly by adding hth, soda ash or acid in quantities depending on the size of the pool. There is a chlorine and acid readind apparatus that you yourself can use to do this work, you can buy it at any pool shop and it is not expensive. In South Africa it costs about R50 more or less equivalent to 4 or 5 euros. Unless you are not at the property full time than you need somebody to do it for you. Leaves, branches, dead insects, anything that can contaminate the water should be picked up immediately you see them in the pool as thay can cause rust once they sink to the bottom and also influence your chlorine levels (do you have a marblelite or fibreglass pool?). I check my pool every single day it takes 5 minutes and it's a good way of having some time on your own. Your pump should also be running for at least 6 hours a day. Again this is easy if you have a timer on the pump. If your pool is covered during winter then you can cut costs as the pump will not have to run in winter, also the cover assists in keeping the pool clean, also the water stays warmer! Easy! The basket next to the pump should also be checked and cleaned at least once a week to keep the water flow into the filter constant. If you have a sand filter the sand should be substituted more or less every 5 years. I don't understand something, you say the pool man does the vaccum? Do you not have a vaccum machine which is connected permanentely to your weir (water inflow towards the filter) and does the job automaticaly everytime the pump goes on? Check at the pool shop, some brand names are barracuda, gemini, etc, it's a long hose and at the bottom it has a round flexible disk with a fin, it has a mouth that eats all the rubbish at the bottom of the pool, I couldn't do without mine. If you don't want to look after the pool yourself which is quite easy and not skilled at all, you must keep the poolman once a week at least.
2. As for the poolman missing one day, it depends on the contract that you signed with him wether you still have to pay him or not. If the contract states that he is to maintain the pool clean and in working order, then it doesn't matter if hemisses one day, you still have to pay him. However if the contract states that he has to come x number of days per month or at least once a week and he misses one day, then you don't have to pay him. Read your contract before you confront him. On the other side, some other times he might have done small things that were not provided for in the contract so you must also do a bit of give and take. But definitely you should mention to him that you are aware that he missed one day. If you don't he will think that he can get away with it and will start missing more days.
I wish I was in Spain, I would come and visit you and teach you how to look after your pool, in Joburg pools are quite common and most property owners look after them themselves. We only call the pool shop if there is something terribly drastic with the machinery.
I hope this helped you, if you have any questions, ask me and I will try to help you as much as possible.
Have a nice summer (when it comes, I believe even Madrid has snow at the moment) and swim lots.
Nelinha