I know that consumption of pork, and clothing oneself with dresses made by pigskin is forbidden. However, is there any harm in using purses, pockets, briefcases, shoes, and cushions, etc. made from pigskin? Specially when I take care not to carry such items to any Masjid and not to touch them with wet hands. Does "tanning" not purify the pigskin while it purifies the skins of "Maitah"?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Muslim scholars differed regarding the matter of dead animals' skin as well as skin of a dog and pig, about whether they become pure after tanning or not. Most of them are of the opinion that pig skin is not pure even if it is tanned. However, the opinion that all kinds of skins become pure after tanning is the preponderant one. Among the evidence for this opinion is the Hadith narrated by Imam Muslim that the Prophet (Sallallahu Alaihi wa Sallam) said: "If the animal's skin is tanned, it is purified" . The same Hadith is narrated in four books of Sunan with the words: "Every tanned skin is pure" .
Based on this Hadith we say that the pig's skin after tanning is pure. So, one may use it. However, if one avoids using it only to take a safe side, no doubt, it is better.
Allah knows best.