What is an aspect . . .
An "astrological aspect" is merely an angular relationship between two points measured and placed on the zodiac. That sounds simple. Since we measure most planets relative to the zodiac circle, and since they are often close to the zodiac plane, this measuring of an aspect or angle works reasonably well.
Or does it? Some planets, such as Pluto, are inclined quite a bit from the zodiac plane, enough so that the planet will often rise over the horizon a half hour earlier or later than its "supposed" zodica degree location.
That being said, lets consider the time you were born. How accurate is that time -- or, if you are doing a chart for someone else, how accurate is their given birth time? On average, for every four minutes of error a different degree could be rising at the Ascendant point. This relates to how much of an "orb" or leeway you are willing to use for an "aspect measurement." If measuring a planet to the Ascendant, and if the aspect is considered a major one, would you allow 8 degrees, 6 degrees, 4 degrees? If the aspect is a minor one, would you allow 3 degrees, 1 degree? Remember, several minutes of error in the birth time used could amplify or diminish the aspect's orb greatly.
With all that now said, lets look at an aspect to a house cusp. What house system are you using? There are several house systems in popular use, and most of these have different ways of mathematically calculating the division process (we are taling about spherical geometry here) to tri-sect the arcs between the major angles. The Placidius system, for example, when you break all of the math down, looks like it tri-sects the semi-arcs in terms of the time it takes for that semi-arc to rise and reach the MC point. Other house systems project their cusps from the MC arc. All of this means that in any one house system, a particular house cusp may be subject to more or less distortion or argument (mathematically) about its calculated placement.
So, how important is that aspect to a house cusp? Everything, it seems, in Astrology has a shaded or considered value. What do you do to minimize them upon your work. Do you maximize potential differences in the combination of practices and processes that you use. Will the results you get in your chart be demonstratable in the next chart you use.
SUMMARY:
I don't want to leave you with more questions and no answers, only to impress upon you that there may not always be a clear answer for a specific case. So, I would keep my use of aspects simple -- conjunctions only! I would limit my aspect orb to one degree for most planets, perhaps 2 or 3 for the Moon. Keep also in mind, that the outer planets often "build up" their influence in a chart over long periods and when something happens it is often due to a "trigger" such as an aspect by the Sun, Moon or Mars, for example. In these cases an aspect to a house cusp can only be an "alert" for you.
Finally, you might consider what I do -- throw out the houses (and signs) and just work with angles and planetary aspects -- they are really dependable. Dave