If you bought a machine straight from another store that was in use prior to you using it you might have an issue. However if you have purchased from a reputable company that has taken the time to perform a general maintenance/refurbishment then I would say no you have nothing to worry about.
There is nothing wrong with used equipment. I sell it all the time. I always suggest buying new espresso machines because you are getting a warranty as well as you're not buying someone else's problems. The espresso machine will be the heart of your location and having a good working machine is key to your survival. Now if you are on a shoestring budget then I can understand buying a used piece of equipment.
Ask the person who is selling it if they have a itemized breakdown of everything they replaced on the machine. Have them show you what they did to it, even if that means making them take off all the panels and point out each piece of what they replaced. I have no issues when it comes to proving what I did when I overhaul/refurbish a machine, it also give me some bragging time about what makes this piece of equipment better than the competition.
Same thing for grinders. Honestly I don't know why anyone would buy a brand new grinder when used ones are available. Most grinder motors are built like a tank and will be the last thing that dies. Your average grinder will only have 4 things that will normally fail over the life of it. Return spring (for doser models), start switch, capacitor, and burrs.