The Mishnah Berurah writes that, when one's fingernails protrude beyond the flesh, one should be careful about keeping them clean under the nails. The dirt that collects under the nails is considered to be a Hasisa (interposition) when doing Netilath Yadayim (the ritual washing of one's hands). He mentions the opinion that one should not allow one's nails to grow long on account of this.
The Ben Ish Hai also writes that one should not grow one's nails because of the problem of Hasisa. However, he adds that there is an additional problem. For Kabbalistic reasons growing one's nails is harmful to the soul. When one has no choice, such as when one is a mourner during the 30 days, one must be particular to clean them daily. Since on Shabbath one may not clean them the usual way, one should wash them with water.
Obviously, for the reasons mentioned above, one should be particular not to let one's nails grow beyond the flesh.
(See Mishnah Berurah 161:3. Ben Ish Hai, 1st year, Parashath Aharei Moth/Qedoshim, Oth 24)
growing fingernails, halacha, protrude beyond the flesh, Chatzitza, Hasisa