Cyclones

Costa rica lies between the Pacific and Atlantic ocean so one would expect extreme weather such as hurricanes to happen often but that is not the case.  Although it rains from May to November, only September and October typically bring the tropical thunderstorms.

These storms tend to bring in high waves (sometimes as high as 70ft.) and non stop heavy rain for hours at a time causing landslides and flooding.  Some areas of Costa Rica receive up to 110 inches of rain during these months.

Sources:

Serendipity Adventures

Online Library

Wikipedia

Sinkholes

One would expect Costa Rica to be plagued by sinkholes because of the amount of seismic activity it experiences but sinkholes in Costa Rica are not a common sight.  The last major one opened up in 2012 due to continuous storms, and it took about three weeks to patch up the 3.5m(l) x 4m(d) hole.

Small sink holes tend to happen only when the country has experienced heavy rainfall or high  magnitude earthquakes occur.

Sources:
Sott.net

Land Slides

Costa Rica tends to have various land slides yearly due to the seismic activity this country experiences. Land slides also tend to happen because the country has a lot of strong rains and storms throughout the year. Researched have a pretty accurate map of where the soil is "weak" and land slides have a high risk of happening, yet people, specially low income indiiduals, build near these areas putting themselves at risk.

Right now researchers are trying to set up better building codes to protects individuals from these land slides. They are also trying to ban the construction of buildings near any bodies of water where the ground is softer making land slides more likely to occur,


Here are a couple videos:
(The first one is in Spanish, but the images tell it all.)

This video here talks about how Costa Rica plans to prevent futute land slides with their Perrilla Module.

sources:

We Love Costa Rica
Tico Times
News.Co