Let me be clear at the outset that what follows applies ONLY to obtaining a visa on arrival (border visa) and is by no means authoritative, but reflects what MOSTLY (almost always) HAPPENS and not what (according to Travel Agencies, armchair "experts" and Mozambique's Consulate's and laws) SHOULD take place.
ARE MOZAMBIQUE VISAS ISSUED AT AIRPORTS AND LAND BORDERS?
Firstly, as a general rule, if you travel on the passport of a country for which Mozambique requires a visa, try to get one before departure. While visas have commonly been issued at airports and MOST land borders (Namoto, Negomano, Congresso, Metangula, Entre Lagos and Mecumbura are not equipped to issue visas), AND THIS IS LEGAL ON PAYMENT OF A 25% SURCHARGE, this is at best a formality requiring nothing more than handing in your passport and approximately $80 (R570, MT 1500). No photos or photocopies required, but proof of booking and return ticket can be asked for. At worst it is a nightmare as (very rarely) the officer on duty can randomly refuse to issue a visa - claiming some or other real or imaginary problem! It must be stated that this is rare, but does make the headlines if and when it happens.
So while there is no absolute guarantee that a visto de fronteira (border or airport visa) will be issued on arrival, chances are actually excellent that you will receive one, even if sometimes a bit of patience and negotiation may be required.
So, to summarize, the regulation that border visas may still be issued (even if you have consular representation in your home country) on payment of 25% above the usual fee, seems sometimes to be ignored by border officials. At the more remote land borders, sometimes the official may simply be too lazy to go through the process of issuing a border visa, or may have run out of visa stickers, or the computers may be off-line.
So, getting a visa at the border or airport is allowed and regulated by law and is most often a formality, it is subject to the vagaries of human nature.
There are a number of categories of visa that can be issued, but I will only deal with the most common ones:
1) Visto de Fronteira
(border visa - usual fee is $50 to $80 but can be a lot cheaper if you pay in Mozambican Meticais or Rands, depending on which that border you use). Note that this is a SINGLE-ENTRY 30-day visa. Despite what the official Moz govt websites may state, double, or multiple-entry visas are NOT issued on arrival. A possible advantage of a border visa, is that it CAN be (by law it should be, but you will be at the mercy of whoever attends to you) extended for one more period of 30 days at Migracao offices in provincial capitals and larger towns within Mozambique.
What does a border visa look like?
I have seen reports of visitors being issued with irregular (illegal) border visas at the Pafuri border post, either due to the official having run out of visa stickers, or due to corrupt practices. So see below for what your border visa should look like.

In order to extend ALL double or multiple-entry visas, it is required that you leave Mozambique and re-enter on a further 30-day permit.
If, for example, you have a six-month multiple-entry visa (of whatever type), you will still have to leave the country before the first 30 days is up, and re-enter on a further 30-day entry stamp.
AT THE BUSIER BORDERS (RESSANO GARCIA, PONTA DO OURO, MACHIPANDA) THERE ARE NOTICES WITH VISA FEES IN METICAIS (MZM), US$, EURO, POUNDS AND RANDS, BUT IT IS BEST TO HAVE METICAIS OR DOLLARS TO HAND. CHANGE IS IN METICAIS AT A POOR EXCHANGE RATE.
Whether at one of the airports or land borders, this (Visto de Fronteira) is the ONLY type of visa that is issued on arrival in Mozambique. The LAW is that the Visto de Fronteira SHOULD only be issued to BONA-FIDE TOURISTS (business-people and work-seekers are not eligible for a border visa) who have travelled DIRECTLY from a country where there is NO Mozambique consular representation, i.e. it would be impossible for them to obtain a visa from. for example, where their flight originates. IN PRACTICE, border visas HAVE BEEN (who knows what the future holds) regularly issued to most arrivals, wherever they come from, BUT if the official just happens to suspect that you are entering Moz to seek work, or do business, then you could be DEPORTED.
If you require a visa for Mozambique, and intend to apply for one on arrival, BEWARE as some airlines and bus companies will not allow you on board unless you can produce a valid visa.
OTHER THAN THE 30 DAY SINGLE-ENTRY BORDER VISA, ALL OTHER TYPES OF VISA ARE AVAILABLE ONLY VIA CONSULATES OUTSIDE OF MOZAMBIQUE:
2) Visto turístico
(tourist visa): fee varies and the initial 30-day period can be extended for two more 30 day periods, BUT ONLY BY DEPARTING FROM, AND RE-ENTERING MOZAMBIQUE - can be done at a land border. The period you have to stay out of the country seems to be arbitrary and ranges between immediate re-entry to five days, from border to border
3) Visto de negócios
(business visa): This can be extended AT A BORDER for two further periods of up to 30 days each. If you will be conducting any sort of business during your trip to Mozambique, this is the visa for you.
Note that, if the purpose of your visit is to seek work, or to take up a job, then you will need to be in possession of a Visto de Trabalho, valid for 30 days, extendable AT A BORDER for a further 30 days.
The official MINISTÉRIO DOS NEGÓCIOS ESTRANGEIROS E COOPERAÇÃO (Mozambican Ministry of Foreign Affairs and cooperation) website link (Portuguese) to visas is: http://www.minec.gov.mz/index.php/viagens-e-negocios/vistos-de-entrada
Another useful website (Portuguese) is: http://www.consuladodemocambiqueporto.pt/vistos.php