If a person was hit by a very short, very intense pulse of gamma ray radiation what problems would that cause?
Based on the wording of your question, I suspect you may actually be interested in the Soft Gamma-Ray Repeater, SGR 1900+14, which produced a celebrated short, intense, burst of gamma rays on 27 August 1998. For that particular event, the answer to your question is "no observable biological effects would result", because, although very intense for what is, after all, a kind of star, the dose was very small compared to the dose due to radiations produced by the Sun and various terrestrial sources. Even a very bright star will not give you a sunburn! However, if the SGR happened to be much closer -- say, less than a light year, instead of thousands of light years away -- then a dangerous biological effect might result.
In science, the everything depends on the actual numbers: "how short?" and "how intense?".
At one extreme, if you were very near a nuclear device as it exploded, an intense pulse of gamma rays would destroy the functioning of your nervous system and almost immediately afterwards cause intense heating throughout your body, sufficient to vaporize you in about a microsecond.
At more reasonable intensity levels, gamma-rays injure cells by creating high-energy electrons throughout the body, charged particles which can disrupt any chemical bond they happen to encounter as they fly along. The delicate chemical machinery of the cell, on which life is based, can thus be either directly destroyed, or else poisoned by the production of myriad possible broken molecular fragments many of which are in effect toxins. Being themselves electrically neutral, gamma-rays typically propagate through matter for some distance with no effect at all, until one of three main possible types of catastrophic interaction occurs:
In all cases, the net result is to transform the incident gamma ray into high-energy electrons (or positrons) which then fly off wreaking cellular havoc as they go. In general the effects beyond this point are similar for all types of nuclear radiation, alpha, beta, gamma, neutrons, and some others. The main difference is that gamma rays, above an energy of a few tens of keV, are very penetrating (considering the part of their behavior before any interaction occurs), so that the damage generally occurs throughout the body.
For pulses with durations of minutes or less, what matters for biological effect is essentially just the total dose, summed over time. A radiation dose to the whole body of approximately 500 rem over a short time will be fatal to 50% of the exposed population. (The rem, or "Roentgen-Equivalent, Man" is the traditional unit of human biological radiation damage.)
The body has a considerable ability to repair radiation-induced damage, so if the duration is long enough (weeks or more, say), the acute effects are reduced. This is at the opposite extreme of the "short intense pulse" you asked about, but is of great practical and economic importance. The extent to which repairs occur due to damage in the 4th class above is only beginning to be understood, and is critical to assessing the biological effects of low-level, long-term exposure to ionizing radiation. The standard hypothesis in the absence of deeper understanding (the linear hypothesis) has been that no repair occurs, so that the risk of inducing a cancer would be simply proportional to the dose, regardless of the duration. Then the number of fatalities due to radiation-induced cancer in a population of, say, 10,000,000 people exposed to 0.01 rem each would be substantially the same as for 3,200 people each exposed to 32 rem. Because of the confusing incidence of natural cancers, the former is very much more difficult to measure than the latter (which might be a few dozen, probably less).