The Placement of the Torah Reading
One will readily notice that whenever the Torah is read at shacharit it is read after the central prayer, the shemoneh esrei, has been recited. Yet, on occasions when the Torah is read at mincha, it is done so before the shemoneh esrei. Why the difference?
It is explained that ideally the Torah should always be read before the shemoneh esrei in order to fulfill the dictum to "la'amod b'tfila b'toch divrei Torah" - to stand in prayer after having first studied words of Torah. Nevertheless, those who set the order of the prayers took into consideration the unfortunate and widespread occurrence of late arrivals to the shacharit service. As such, it is widely suggested that the reason the Torah reading of shacharit was placed after the shemoneh esrei was due to the concern that too many people would end up missing the Torah reading had it been placed at an earlier point in the service.
Indeed, there are many synagogues that inadvertently encourage this trend by posting two, or even three different start times for their shacharit service. For example, some synagogues post a "berachot" time, a "hodu" time, and a "barchu" time for their shacharit service in order to inform congregants what the pace of the service is and at what time each of these prayers will be recited. Unfortunately, some individuals take advantage of this information and purposely arrive late to services rationalizing their behavior as being on time for the "important" parts of the service. This phenomenon forces one to have to skip parts of the service in order to be able to recite the shemoneh esrei together with the congregation – a habit which is censured by all halachic authorities.
In contrast, however, it seems that most people make a special effort to arrive on time for the mincha service. This is likely because the primary function of a minyan is in order to allow everyone to recite the shemoneh esrei together. Arriving even a mere few minutes late to mincha, therefore, would undermine the entire purpose for having come in the first place! Since people are in the habit of coming on time to mincha it was felt "safe" to place the Torah reading immediately at the beginning of the service before the shemoneh esrei, which is truly its ideal slot.[1]
[1] Minhag Yisrael Torah 135:1