The difficulties are as follows:
Although the definition of "country" may seem obvious, there are occupations of one country by another, stamp issued by areas in rebellion, reunifications, and regions that have issued their own stamps for one reason or another. A classic example is Germany; unified from many smaller entities, then divided into multiple zones of occupation at the end of World War II, then divided into West Germany and East Germany, then reunified. Catalogs typically treat West Germany as part of a single sequence under the name "Germany" while giving East German stamps their own numbers.
The definition of "postage stamp" can also be problematic for catalogers. For instance, some countries have issued adhesive labels purporting to be postage stamps, but which had the "cancel" printed directly on the stamp and shipped to dealers, without ever being sold to the public for use on letters. The treatment of these has long been a vexing issue, and catalogs vary greatly on whether to list the stamps. A related issue is a small number of extremely rare stamps that may or may not be old forgeries; the assignment or removal of a number is a key step in the consensus as to their authenticity.
Philatelists typically identify more types of stamps than do the governments issuing them. Changes of perforation, watermark, often occur without any official notice, as do printing errors. In a few cases, even the date of first issue of a stamp has no surviving record.
The issuance of multiple types on a single day is an old practice, but usually these were different denominations, and could be numbered in ascending order of value. More recently, it has become common to issue a group of stamps with related designs and the same denomination on the same day.
Finally, it is common for the stamps of a definitive series to be issued one or a few at a time, as postal rates change. Logically, they are part of a single group, with a unified design theme and a sequence of values, even though ten years or more may have elapsed from the first to the last. The same reasoning could be applied to special-purpose stamps such as airmail or postage due stamps.
Numbering of stamps cannot be a purely mechanical process; it is a complicated undertaking that requires some editorial judgment. Over time, stamp numbers become a shorthand for collectors and dealers; in the United States, the Scott catalogue number "C3a" is instantly recognized as the Inverted Jenny.
The Scott system assigns plain numbers for regular mail stamps, and uses capital letter prefixes for special-purpose types, such as "B" for semi-postals and "C" for airmail. The numbers are generally consecutive; there are gaps among older stamps, where some numbered types were later renumbered, and among newer stamps where Scott has left numbers unassigned in the anticipation of additional stamps in a series. If more stamps than expected appear, Scott will add a capital letter as suffix, or if the change is very recent, it will renumber stamps. Minor variations, such as shades or errors, get a lowercase letter; so the "C3a" above indicates a variation (error in this case) on the third US airmail stamp.
The Gibbons, Yvert and Michel catalogs use different arrangements for numbering regular and special-purpose types, and attach different importance to variations in paper, perforation, watermark and other types.
Because of its commercial importance the publishers of the Scott Catalogue claim copyright on their numbering systems, and grant only limited licences for their use by others. The inconsistency with which Scott enforced these licences resulted in a lawsuit by Krause Publications (publishers of the Minkus Catalogue) for copyright infringement. After Krause filed a defence the suit was settled out of court, and Krause continued to reference the Scott numbers. It has been speculated that Scott was not successful Attempts by philatelists to establish an alternative have not yet been successful.
In general, governments have not tried to number their own stamps. The People's Republic of China is a notable exception, having inscribed most of its stamps with a unique numbering system since 1949.