From the Citadel, GRRM replied to a similar question in this way:

> **5) Why were men like Meryn Trant, Boros Blount, Preston Greenfield and Arys Oakheart ever accepted as White Swords? Nobody thinks much of
> their skill.**
> 
> **GRRM:** Sometimes the best knights are not eager to take such stringent vows, and you have to settle for who you can get. Other
> factors also enter into the choices -- politics, favoritism, horse
> trading, rewards for past service, etc. It's a plum appointment for a
> younger son, or a knight from a minor house. Less so for the Great
> Houses. Also, Robert had five vacancies to fill all at once, an
> unusual situation -- imagine the nominations we might get if six of
> the nine members of the Supreme Court all died within a few months.
> 
> Institutions like the Kingsguard change over time. The original
> Knights of the Garter were warriors all, the strongest, bravest,
> deadliest men of their time, with an average age under thirty. The
> present Knights of the Garter are octagenarians, and their parades are
> processions of wheelchairs and walkers.<br><sub>[So Spake Martin - The
> Kingsguard](https://www.westeros.org/Citadel/SSM/Entry/The_Kingsguard)</sub>

He similarly absolve Jaime and Barristan on claiming pardon on technicalities. 

>**4) Does the oath of a Kingsguard include to serve _whoever_ is the king, even if the new king rebelled against the old one, or did Jaime and Barristan _choose_ to continue their service as Robert was crowned?**
>
>**GRRM:** The oaths did not envision rebellion, actually. Robert pardoned Barristan and Jaime, and they accepted the pardon and continued to serve.<br><sub>[ibid](https://www.westeros.org/Citadel/SSM/Entry/The_Kingsguard)</sub>

So it seems that political motivations paved the way for more controversial appointments when we look at the members. The criteria over the years for picking Kingsguards seems to be, judging by the common traits, the following:

 1. The candidate must be good with sword, lance or spear.
 2. The candidate must not come from a too influential family although exceptions like Jaime Lannister, Prince Aemon, Gerold Hightower, Raymont Baratheon etc exist. 
 3. The candidate must be honourable.

We also have precedent where KG cloaks are used as an incentive to get political support of different houses e.g. Loras Tyrell or Young Griff holding out white cloaks. So politics definitely plays a role. 

 

 - Preston Greenfield is likely a kin to Lord Greenfield who is a vassal to Lord Tywin Lannister, Robert's father-in-law. He seems to be appointed to appease Westerlands and Lord Tywin. The family has no significant political power. 
 - Ser Arys Oakheart comes from a Targaryen loyalist family from the Reach. This seems to be a conciliatory gesture towards the former loyalists just like Aegon III's seven included members from both Black and Green families. The family is a major one but not one of the Great Houses. 
 - Boros Blount comes from a minor house from Crownlands. Seems to be the same case as Oakheart. The family has no significant political power. 
 - Mandon Moore comes from the Vale and since he came to KL with Lord Jon Arryn, it seems Robert appointed Moore on Lord Arryn's request as a reward for Vale's support for Robert in the war. The family has no significant political power. 
 - Meryn Trant comes from a minor family in Stormlands, Robert's own ancestral holdings. This seems to be a case favouritism or reward for service of the family. 
 - Jaime Lannister, presumably pardoned to bind Lord Tywin to Robert's cause. The significance for making sure that most KG came from minor families should become clear from Jaime's case. The political considerations in case of powerful families are too huge to let honour be a nuisance. 
 - Barristan Selmy, technically not in any wrong at all according to the author. He also comes from Stormlands and is the son of the Lord of Harvest Hall, a key vassal to Baratheons.

Kuhl's comment about not seeing the flaws of prior KG is worth noting. We condemn Robert's Seven for standing by Joffrey as he lurched from one evil to another, even beating his betrothed for him. But Aerys' seven, who are considered shining paragons of chivalry, did nothing more than Joffrey's seven did as Aerys tortured his wife in a bestial manner even though they were sworn to protect the women (Jaime tried to intervene once when he stood guard outside the Queen's door but he was stopped by his comrades who said they were sworn to defend the Queen but not from the King) or burnt his "opponents" even though they were sworn to defend the helpless. Maegor's and Aegon II's seven did the same (Although there are rumours that it was the KG who killed both of them eventually).


So in conclusion:

 1. Robert faced the virtually unprecedented situation of filling five vacancies. The only time something of this magnitude happened before was when the order was founded and Queen Visenya picked 7 men. He was bound to make some mistakes.  
 2. Best suited men might not have been eager to take the strict vows so Robert had to make do. 
 3. Political considerations like rewarding his supporters, appeasing the former enemies, doing a favour to crucial allies played a role in the appointments.