Buying a used piano can be daunting task and large investment. You should make sure you know what you are buying before you buy it. I think that you are taking a very smart approach by inspecting it yourself and then having a professional look at it. When inspecting a piano I would search for the following things.
On first glance I would inspect the exterior:
If the pedals have just gone a bit limp it is usually because they have been detached from the surrounding parts (which is usually a very easy fix, depending on the accessibility of the piano). If the pedals don't move at all you might have a bigger problem at hand. A great way to look at pedal function is to make sure the hammers and dampers are in view when testing pedals (do dampers raise, action shift, etc.).
Watch out for excessive damage on the keys because it can usually mean that not only is there damage on the outside, but something might be going on inside too. Strike every key and listen for buzzing, dead notes, notes that sounds like they strike twice, and sticky notes (the keys don't pop back up after you play them). Most of these issues can be remedied and fixed if you are willing to spend some money on your piano.
Weather damage (such as humidity) is often a suspect in a piano's bad health. Cracks, scratches, discoloration (from sun damage), and warped wood can all be viewed from the outside, but it usually means the inside wood is not looking any better.
Next (if accessible) I would check out the interior:
The soundboard is a wooden plate at the bottom of the case (in a grand piano). In an upright piano, it is at the back of the instrument. If any reinforcement ribs have come unglued, they will vibrate against the soundboard, causing for even slight buzzing when the keys are pressed. Also look at the bridge (where the strings touch the soundboard). If the bridge is cracked, uneven, or unglued from the soundboard, buzzing will occur, and further damage is likely to follow.
Look for deep grooves on the hammers caused by strings. Are they worn to the nub? If the felt on the hammer appears to worn all the way down play the note and listen for a harsh and blunt tone. The felt on the hammers cannot be re-glued due to the way they are originally applied.
The Pin block
If the pin block wood is damaged, the tuning pins can loosen, causing buzzing sounds and bad pitch (it can make one note sound like two due to one string going slightly out of tune). Keep an eye out for cracking in the wood block and loose pins. Also make sure that there is no rusting on the strings or tuning pins.
Here are some videos that could be helpful as well:
Inspecting a piano
Appraising a piano
Buying a used piano
Here are my sources:
If it looks like this I would recommend not buying it. :)