Mostly limited to Asuncion, many of the public streets have unofficial parking attendants who will no doubt approach you as you are parking and demand some money. The ruse is that the money will secure your vehicle from any mishaps. However I´m told that most of the time it is the very same people who cause the damage if they are not paid.
A couple years ago, this was actually made legal so the police do nothing about it and it has become quite common place.
The locals that I was with told me it is recommended to tell them something like you have no change and that you will pay when you return. Chances are that when you return, they will have collected their daily personal quota and will have gone home so you´ll be left in peace. If you do pay them, only give them a couple thousand Guaranies.
Of course, around some special events or areas (like shopping mall garages) actually have official attendants, which usually wear some sort of vest and name badge.
The heat in summer in Asuncion can be oppressive. Prepare yourself, wear a hat and something light. There are some nice local cotton shirts you can buy in Paraguay. Winters are cooler and more 'agradable'.
The runway of the International Airport is not to reliable, as this Iberia DC10 found out in 1981. Nowadays the surface is even more slippery.
After a summer rain (January) there is widespread flooding. Sewerlids will come off and the sewerpipes act as fountains at the lower roads. Don't be surprised when you end up in 50 cm of water.