Hi Polostar,
I've been spending a month or two a year here for the last 10 years (buying polo ponies), normally rented sight unseen from the pics on the internet and never had a problem. I agree that a months deposit is normal, us polo players can do a lot of damage if the party gets out of hand! I've now been here for the last nine months and have encountered friends who have had problems. My tips are;
If you can afford it rent in Puerto Madero because everything is new and everything works!
Go to an agency with a lot of stock on its books, because if they try and screw you, you simply tell them that under every advert they post you will put a disparaging statement. You can kill their business like this!
Be very clear about what you want and put it in writing. In argentina it is much easier to say, "I told you I needed this, I expect you to sort it out tomorrow" (80% chance of success) than "I thought the apartment would come with more plates, would you be able to buy some more tomorrow" (10% chance of success).
That being said, and to counterbalance the invariably negative comments I see on this site, I have never once had a problem here myself, never had any unforseen expenses removed from my deposit and never had a dodgy landlord.
Agency wise i have used a bunch. The ones I remember are apartments BA and BYT argentina, both of which I have used several times.