After some extensive searches, I found the following information on the importance of degrees in a chart. I hope it's applicable here:
The first thing to note is the placement of the planets. If most of the planets are on the east (rising), the person is working on Destiny Sowing. If most of the planets are on the west side of the chart, the person is working on Destiny Reaping. Note whether the majority of the planets are above (outer world) or below (inner personal growth) the horizon. Configurations are very important, mainly T-squares, grand trines and grand crosses. Check for planets at the degree of the Nodes and at critical degrees. The critical degrees are 0, 13 and 26 of cardinal signs; 4 and 17 of mutable signs; 9 and 21 of fixed signs; and any planet or cusp at 29 degrees of any sign. The Lords of Karma at 15 degrees of fixed signs show a fated chart, especially difficult if the Nodes or Ascendant are also at 15 degrees. (Source:
http://www.azastrologers.org/Articles/CollinsFamousStars.PDF)
-----
Classic critical degrees are 0, 13, and 26 degrees of the cardinal signs (Aries, Cancer, Libra, and Capricorn); 8-9 and 21-22 degrees of fixed signs (Taurus, Leo, Scorpio, and Aquarius); and 4 and 17 degrees of mutable signs (Gemini, Virgo, Sagittarius, and Pisces). These are considered sensitive, and sometimes strengthening, points. If a natal planet is found in a critical degree, that planet is emphasized and assumes more power in the life of the native due to its placement.
Many astrologers consider 0 and 29 degrees of any sign critical degrees as well. The 0 and 29 degrees are more crisis-oriented points, especially in predictive work. (Source:
http://www.cafeastrology.com/criticaldegrees.html)
-----
Taken from the Hindu concept of Vedic Astrology, it is believed that there are degrees of a sign at which it is most fortunate to have a planet positioned.
Critical Degrees are derived mathematically by dividing the Zodiac by the Moon's average daily motion. These positions within the Houses are known as the Lunar Mansions.
The Cardinal Signs -- Aries, Cancer, Libra and Capricorn -- can smile if there's a planet in their birth chart positioned at 0, 13 or 26 degrees. The Fixed Signs -- Taurus, Leo, Scorpio and Aquarius -- will be happy to see a planet sitting at 9 or 21 degrees. The rest of the Signs are Mutable; Gemini, Virgo, Sagittarius and Pisces are quite fortunate to find a planet in their natal chart hovering at 4 or 17 degrees. (Source:
http://karma.astrology.com/critical.html)
-----
The 30 degrees alloted for each zodiac house can be divided into three groups of ten degrees each as 0 to 9 deg, 10 to 19 deg and 20 to 29 deg. These divisions are termed as Decanates. The first ten degrees are called as the First Decanate, the second ten as the second Decanate and the third ten degrees are the Third Decanate.
The first decanate of any sign corresponds to to the sign being studied so that the first deanate of Aries will relate to Aries. The second Decanate of any sign takes on the characteristics of the next sign in the same element and hence the second decanate for Aries is Leo. The third decanate of any sign is the last sequential sign within the same element and so for Aries it would be Sagittarius.
Each decanate in a sign gets the traits or qualities of the sign ruling it. The first decanate is tHE strongest and it corresponds to the double strength of the sign. A person born during the second and third decanate will be less typical of the sign udner consideration.
The decanates are said to have psychological and physical significances and are related to the mind, body and soul.
0 to 9 degrees- This decanate corresponds to the physical side and relates to the body. When a person has many planets in these degrees they would be practical, materialistic and sensible. These degrees are very powerful. The 0 deg represents the beginnings and the 9th degree represents the endings and the physical aspects.
10 to 19 degrees- This decanate corresponds to the mental or the Mind side. Those with more planets in this decanate are said to be intelligent and concentrate more on mind activities. They are logical thinkers and are well-informed about the latest trends. Degree 10 represents new pursuits and degree 19 represents the peak of mental activity.
20 to 29 degrees- This decanate corresponds to the spiritual aspects of a person. When many planets or in this decanate, the native would be spiritually inclined. Some might have problems like addiction and self-destruction. Degree 29 relates to the spritual peak. (Source:
http://astrology.findyourfate.com/astrology-decanates.htm)
-----
A critical degree is a degree in the horoscope that is felt to have significance. The concept of the critical degree is based on Hindu technique of Lunar Mansions, which subdivides the horoscope into 13 degree segments, which is the Moon's average daily motion. When a planet or point falls on a critical degree it is often believed to be strengthened because it is on the cusp of the 13 degree house sub-division. The critical degrees are as follows:-
* Aries - 0, 13, 26
* Taurus - 9, 21
* Gemini - 4, 17
* Cancer - 0, 13, 26
* Leo - 9, 21
* Virgo - 4, 17
* Libra - 0, 13, 26
* Scorpio - 9, 21
* Sagittarius - 4, 17
* Capricorn - 0,13,26
* Aquarius - 9, 21
* Pisces - 4, 17
(Source: http://en.wikipedia.org/wiki/Critical_degree_(astrology))