Focus
Focus checking will generally be done either in the back of the camera or in Lightroom after the images have been loaded onto a computer. If a photo is out of focus, we will assess whether it is saveable in photoshop or not. If it is, I use photoshop's unsharp mask to regain as much sharpness as possible. This is generally not done for most shoots as the effort and time that goes into it could probably be saved by simply using a different frame.
Exposure
To check exposure, the first port of call would be to check the histogram.
An Adobe Lightroom Histogram
On a histogram, the x axis shows from black to white, and the y axis shows the amount of that shade in the photograph.
To check that the exposure is correct, a histogram should stretch from one end to the other to ensure that all the shades are present. However, if the histogram is mainly on one end, that means the photo is either under or over exposed. For example:
When the histogram touches the edges, this means that some information is lost due to over or underexposure. The darker end of a histogram is easier to recover than the highlight end due to the nature of information collect and how it works.
On a lens, any dust or bits of flush or scratches will potentially leave a mark on the photograph. Generally, these are not visible when the photo contains lots of detail, however if the photograph contains lots of blank space they will show up more prominently. These can easily be removed using either the spot tool in Lightroom or the Healing Brush in Photoshop.
Chromatic Aberration
On some lenses, Chromatic Aberration occurs at wider angle zooms (e.g 16-20mm on a 16-35mm lens). Chromatic Aberration shows as a coloured glow around certain objects, mainly at the edge of the frame. This can be corrected using the Chromatic Aberration Correction option in Lightroom. Previously, the tool was a lot more complex - requiring the editor to manually select the colour of the aberration. However, Adobe have recently released a new version of Lightroom (Lightroom 4) which includes an updated chromatic aberration correction tool. In the updated version, there is simply a check box to click and it gets rid of any chromatic aberration in the photograph.