Hardware checks:
* Dead pixels - Install an app like Screen Test to better detect any dead pixels. One or two in out of the way places might be acceptable depending on your tolerance level. But no dead pixels, which is the norm, is what you want.
* Speaker quality - Play some audio content, preferably something with a little bass to it, to determine if the speaker is bad or blown. If you hear distortion at higher volume levels, there is a problem. Don't expect a magnificent listening experience even if the speakers are okay.
* Headphone jack - Plug in headphones (push very firmly to seat properly) to make sure everything is normal.
* Screen lift - The infamous screen lift issue is an easy check. If the screen on the left side of the Nexus 7 is protruding above the bezel, you have screen lift. However, there are various levels of this problem, some very bad and some rather minor and acceptable. If you put pressure on the left side of the screen, and with relative ease you can feel the screen being pushed down a fair amount, and also feel and hear a creaky effect, then this is rather bothersome screen lift. Depending on your tolerance level, it might be worth a return.
* Charging system - Make sure the unit charges properly. Inspect the included wall charger and USB cable for any obvious defects.
* Camera - Test the camera by downloading Camera Launcher for Nexus 7. If you see yourself, it works.
* WiFi, Bluetooth, NFC, GPS - These will all likely work just fine, so testing them isn't too important. You've already verified WiFi, which is the most important of these, so you could try to connect Bluetooth with a headset or your car. Testing NFC is more of a challenge, I'd think. GPS should be a relatively easy check, but there are free GPS testing apps available if needed. Again, it's unlikely there would be a problem with any of these.
* Miscellaneous - It's also unlikely there would be a problem with the gyroscope, accelerometer, microphones, magnetic field detection, and light sensor. But there's a simple, free app called AndroSensor that will quickly show you if these items are doing something. That doesn't necessarily mean that they're doing them right, but at least you'll know they're active.
Software checks:
After you've done all your tests, which would require that you actually initialize the Nexus 7 and register it to your Google account (to install the testing apps and play audio), there's really not much else to check in terms of software. If you were able to successfully use the N7, then it works!
At this point, whether you decide to return the device or keep it to give as a gift, you'll want to do a Factory Data Reset: Settings > Backup & Reset > Factory Data Reset. This will wipe out all data, downloaded apps, settings and accounts (yours and perhaps the previous owner, if they didn't do a reset), and return the N7 to factory settings with no personal data, just as it was when it came out of the box the first time.
If you gift it, give it a full charge before wrapping it so that the recipient can use it right away without having to be plugged in. Also, hopefully the seller provided a copy of the original purchase receipt from when the N7 was purchased new. This might be helpful if you need to obtain warranty service from Asus. The warranty would only be good for the stated time period beginning from the date of original purchase. I'm sure you could get service without the receipt, but having it might make it easier, and would also verify the warranty starting date.
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