Outside of the standard SSD drives, DO has not had any major data breaches that I'm aware of. That's a pretty big one. At this point recommending Linode to a company I work for seems borderline negligent considering their security history.
DO had the issue where you could delete a droplet without scrubbing the disk. So the next person to create in that area could read the disk and recover any data from it.
That's a slippery slope. By that logic no company can be critiqued for security failures. Linode was storing their shell passwords in clear text. To me that's where I draw the line.
On the other hand, if there were good alternatives to OpenSSL the community probably would be talking about considering them right now.