There is a custom to refrain from bitter, sour or tart foods on Rosh Hashanah, to symbolize our hopes for a sweet, pleasant year. The Talmud teaches that "Simana Milta Hi," which means that symbolic acts have significance. One must therefore not belittle the customs regarding the foods eaten on Rosh Hashanah as symbols of our prayers for the new year, as these customs are very significant and indeed have an effect.
There is a common practice to eat a pomegranate on Rosh Hashanah, as the abundant seeds symbolize our hopes that we will come before God with abundant Zechuyot (merits). Interestingly, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that on Rosh Hashanah one should eat specifically a sweet pomegranate, and he emphasizes this point several times. Of course, the pomegranates we have today generally have a bitter, pungent taste. It appears that in Baghdad, where the Ben Ish Hai lived, they had sweet pomegranates. In any event, in light of the custom to refrain from bitter foods on Rosh Hashanah, it would seem proper to dip the pomegranate in sugar to at least diminish its pungency.
It is also interesting to note that the custom of the Ben Ish Hai on Rosh Hashanah was to dip an apple in sugar, and not in honey. Perhaps this custom was based on Kabbalistic teaching. Regardless, everyone should follow his family’s custom in this regard.
It should be noted that the symbolic significance of the apple on Rosh Hashanah extends beyond the simple fact that it is a sweet food. The Zohar refers to Gan Eden as the "Hakal Tapuhin Kadishin" – "the orchard of sweet apples." The apples eaten on Rosh Hashanah thus symbolize not only sweetness, but also Gan Eden, which is certainly an auspicious sign as we begin the new year. Furthermore, the apple has a pleasing appearance, a pleasing fragrance and a pleasing taste. It is pleasing and enjoyable in every which way, symbolic of our hopes that the new year will bring joy and success in all areas of life. Furthermore, the Ben Ish Hai explained the significance of this custom on the basis of Kabbalistic teaching. During the period from Nissan until Tishri, we are under the influence of the Sefira ("emanation") of Malchut, which is the lowest Sefira and receives its strength from the higher Sefirot. Once Tishri sets in, we move into the Sefira of Tiferet, the highest Sefira, which gives to the lower Sefirot. The Sefira of Tiferet is the Sefira of Yaakob Abinu, who represents Torah, and who transmitted the power of Torah to subsequent generations. Tiferet is also associated with the attribute of "Emet" (truth), and on Rosh Hashanah we stand in judgment, which is based upon God’s attribute of absolute truth. The apple, the Ben Ish Hai writes, is associated with the Sefira of Tiferet, and we therefore eat it on Rosh Hashanah, which marks the point of transition from the Sefira of Malchut to the Sefira of Tiferet.
Of course, the vast majority of us are not versed in Kabbala, and thus do not truly understand these concepts. Nevertheless, they demonstrate the depth and profundity of these customs that we observe on Rosh Hashanah. Besides the plays on words, such as "Yitamu Son’enu" for the "Tamar" (date), and "Yikartu Son’enu" for the "Karti" (leek), there are much deeper concepts underlying these customs, and we should therefore observe them in accordance with time-honored tradition.
Summary: It is proper to refrain from bitter and sour foods on Rosh Hashanah. Pomegranates should preferably be dipped in some sugar before they are eaten on Rosh Hashanah, because they otherwise taste pungent. Some have the custom to dip the apple in sugar, instead of honey, and each person should follow his family’s tradition. The customs regarding the special foods on Rosh Hashanah are based upon profound Kabbalistic concepts and thus should not be belittled or neglected.