Here's one way to simulate a bad scan of an old document. I'm using the GIMP here, but you should be able to do all these steps in Photoshop too.
Step 1: Start with a suitable-looking picture.
If you're trying to emulate an old hand-written document, remember not to be too precise. Hand-position lines, vary the font size (and/or use several fonts), rotate or stretch individual letters, maybe even apply a slight perspective transform to whole paragraphs of text to make the lines slant a little. The picture above is just a quick test.
Step 2: Make some noise.
Make a new layer and fill it with some procedural noise. Here I have a mixture of low-frequency noise (generated with the Render → Solid Noise filter) to simulate a non-flat paper surface, and high-frequency noise (generated with Noise → RGB Noise) to simulate paper grain and scratches. In hindsight, I probably should've made the low-frequency noise even lower in frequency, but this is good enough for a quick demo.
Step 3: Blend the drawing with the noise.
Here, I just set the noise layer's opacity to 50%, and flattened the entire image for the next step.
Step 4: Blur everything a little.
It might not be obvious from the final result, but this is actually the crucial step to making the scan look realistically bad. Basically, we're blurring the image to simulate the imperfect optics in the scanner. Here, I've applied Gaussian blur with a radius of 2.0 pixels, but you may want to play with the radius to fine-tune the results.
Step 5: Adjust levels.
Just open the Levels tool, pull down the white level until the background looks mostly white, and then raise the black level until the text and lines look mostly black. (This is pretty much exactly what scanners do in text mode.) Voilá, one bad scan ready to go!
You may also want to consider applying some Unsharp Masking after the blur; combined with the Levels adjustment, this will create a distinctive effect where faint lines vanish near thicker lines. (It also undoes some of the effect of the blurring, so you may want to use a bit more blur to compensate.) I didn't do it here, because the result looked good enough without it, but it is a feature often seen e.g. in old photocopied documents.