The targeting interval either amplifies or dampens spikes in the hash rate's effect on the overall difficulty.
Having a shorter targeting interval allows for the difficulty to adjust quickly to changes in the hash rate, however there is a greater possibility of an attacker pushing the difficulty to crazy heights with less hash power.
Having a longer difficulty dampens this effect, but at the same time a drastic drop in hash power will leave the network hurting for a longer period of time, since more blocks need to come out before the network recalculates the difficulty.
In the end it's more or less the same, shorter intervals can have their difficulty altered more easily, but is less lasting; longer intervals makes altering the difficulty more expensive, but is longer lasting.
It is possible for an attacker to do this, with the development of ASIC there were many who took advantage to attack TRC and other SHA based coins. This would not always be an attack on purpose. There are several miners and pools (such as multipool.us ) which will mine the most profitable coin, and doesn't pay much attention to how it's changing the difficulty. For example, if AB Coin were to inexplicably multiply in price 100x, the miners would all be trying to get AB Coin and would consequentially raise the difficulty 100x as well. Once this difficulty has been reached, there is no more benefit to mining AB Coin over another coin, and miners would go find another which is trading higher than it's difficulty. This leaves AB Coin in bad shape, as it's regular mining group is only 1% of what it used to be (in terms of blocks produced).