Every Critique from this group is expected to be in-depth and thorough. As such, every critique should be more than one paragraph long. How a critic chooses to present a critique in style and so forth is up to them. Remember, you're doing this to help out a fellow artist; give tips and pointers for problem areas and don't forget to mention the positive aspects of a piece.
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Typical things you'll want to address in Critiques:

Form/Composition

Color

Contrast

Fluidity (how the eye moves along the piece)

Proportion

Subject Matter/Social Context

Form/Composition
Taking in account the entirety of the piece, how the placement of the main subject is in relation to the background and other focus subjects. Here are a few examples of what you would ask yourself while critiquing with the main question: What Makes This Artwork Interesting?

Odd angles
Interesting lighting
Focus on a not normally focused detail
The expression of the focus (if a face)
Placement of the figure in reference to the total piece (just being in the middle tends to be boring)


Color
Color harmonies or clashing, the overall use of color or lack of color in black and white or sepia works to convey an emotional state. Here are commonly used color references:

Monochromatic (one color + highlights/shadows)
Complimentary (colors that when mixed makes brown ie: green and red)
Clashing (colors not normally meant to be with eachother ie: neon green and lemon yellow)
Primary (red, yellow, blue + highlights/shadows)
Secondary (green, orange, violet + highlights/shadows)

When considering color, ask yourself this:

Do these colors help convey an emotional response?
Do these colors hurt the art rather than help it?


Contrast
Contrast is determined by how dark the shadows are and how light the highlights get. In photography this is determined by lighting and filters, in dry/wet media, it is determined by how dark/light the artist dares to go. In pencil especially, contrast is important to show detail and to make things appear 3D. If the pencil isn't dark enough, the picture will have a very low contrast and details will be lost.

Note: Contrast will differ from critic to critic by their own preferences, however it is shown that professional artists tend to go for higher contrast than lower.

Fluidity
Fluidity is how well the subjects of the work come together and lead the viewer to each subject, being a part of composition/form. If the eye doesn't follow to the next part by color, actual sections of the primary subject, or any other binding force, it just seems to float and doesn't have any ties to the rest of the picture.

An example of which would be the hair on the main subject, being a portrait, flowing into the background and touching a flower, which would be the second subject.

Proportion
Proportion is how something relates to something else. When a subject is out of proportion with the picture, it tends to look uneven, or even noticeably wrong. Proportion is very important to anything that deals with non-abstract subjects.

In photography, proportion is rarely a problem unless the camera isn't working properly. Examples of proportion in action:

Parts of the body in relation to the rest of the body (like head in relation to the body)
The size of a subject in relation to the size of its secondary subject (like a bee on a flower)

Subject Matter/Social Context
In the majority of cases, the subject matter of a piece of art is made to convey a message or envoke an emotion to or of the viewer. The availability to reach the viewer is Social Context. If this piece was made for all to enjoy or for a certain genre that only a few would understand. The questions you would ask yourself include the following:

What is the message/emotions that you as the observer take away from this image?
Do you think that this was what the artist's intent was, and if so, how succesful was it?