Regarding possible "harm", perhaps their biggest risk vector is they don't support any variant of STP. I.e. you can create L2 loops.
Yet, consider, if you read the reference @MHM Cisco World posted, Cisco also sells a series of unmanaged (non-smart) switches, ranging from 5 ports to 24 ports. If such switches are network death traps, how can Cisco, in good conscience, sell such diabolical devices?!
Or, consider, somehow, smaller networks, like under 100 employees, (successfully) operate day to day using such fiendish switches.
(Why I even remember, decades, ago, recommending upgrading such a sized network from unmanaged 10 Mbps hubs to smart/managed low end Catalyst switches. Push back was, what we have works, and it did. But the company was growing, and avoiding the 10 Mbps hub 5-4-3 rule and/or being able to capitalize on full duplex and/or 100 Mbps [for which rules of extending were much more restrictive than the 5-4-2 rule, like max of 3 segment if using Class II FE hubs], were some of the benefits that finally convinced management, upgrading was worthwhile.)
Don't misunderstand, better switches, are just that, better, but you need to balance cost of the "better" to your actual needs and/or risk to not having the "better".
Not to pick on (well not too much) @Leo Laohoo's anecdotally story, if we relate the story of the Titanic's sinking, we might draw the conclusion you should never board a ship with too few lifeboats. Although that appears to be "good" conclusion, I'm sure the survivors would believe that (like Leo being a survivor of his A Night to Remember), especially the very, very few that survived without being in a lifeboat, it may not be, for multiple reasons, as "good" as it appears at first glance.
(If you want to ponder on the Titanic's sinking, first analyze what many of the victims of the Titanic sinking actually died from, then also review the Andrea Doria and/or the Costa Concordia sinkings and how enough lifeboats for everyone aboard, mattered, or not, for them. Oh, and for something more modern that being on a ship, when's the last time someone provided you a parachute when you boarded a commercial airliner?)
So, my point to the foregoing, making this kind of decision isn't just based on "harm", but also on the impact of the "harm" and how likely such "harm" might occur. Using such information, you can make a more rational decision whether you should work to avoid the possible "harm" (like never fly [and hope an airliner doesn't crash on you - which has happened - although, very, very rarely], or just accept the potential "harm" [you might also plan for how to minimize "harm's" impact if it does happen]).
Let's talk a bit more about the most possible likely, the "harm", a L2 loop causes.
Well, first consider you have Enterprise level L2 edge switches, and someone cross links two ports, whether using a patch cable or a unmanaged switch. Both have created the same L2 loop. Both, if you don't have portfast enabled, but do have STP enabled, STP should have blocked the second port from joining the L2 topology, i.e. L2 loop is prevented.
If portfast is enabled, and STP is enabled, hopefully (there isn't a 100% guarantee in this case), STP will "see" the L2 loop created and again block a port.
Or, you have your unmanaged switch connected to your managed switch, and someone creates a L2 loop on the just that switch. The problem with that is, possibly that local unmanaged switch will flood the uplink to the managed switch, at full wire rate. That, alone, shouldn't be much worse than a host, or hosts, driving uplink to full wire rate. However, if the traffic being flooded toward the uplink has no known destination within your managed switch network, the managed switch network will flood that traffic to all the ports in the same L2 broadcast domain. Basically, very much the same effect if I had a single host transmit broadcast packets as (continuous) wire rate. I.e. again, same effect, even if using all managed switches! However, an unmanaged switch doing this might be by "accident" whereas the broadcast flood is more likely an intentional DoS, although, possibly, not intentionally done by the host's user. Another aspect of the unmanaged L2 loop flood, it may be creating a unicast flood, which some managed switches, may not have rate caps for as they sometimes offer for broadcast floods.
So, I would say that using an unmanaged switch does increase the potential for a L2 loop "harm" but by how much, that's very difficult to say. (Do your users typically cross connect RJ45 wall jacks?)
Above, I mentioned you can plan to mitigate "harm". Well, if you're running unmanaged switches on edge ports, you might police those ports, that they cannot run wire-rate 100% of the time and/or if managed edge ports are gig, run them at 100 Mbps and/or limit the size of VLANs supporting such edge ports (with the latter, you might even have each such edge port in its own VLAN). I.e. The forgoing won't preclude there being L2 looping "harm", just that it minimizes the how "harmful" the harm is.
Have you ever heard the saying, there's risk to getting out of your bed in the morning? Yes, there is, but we often deal with risk, of various degrees, all the time.
Again, other posters are correct, there are many reasons why you don't want to use unmanaged switches, even at all, and if managed switches could be obtained without any additional cost to obtain or maintain or operate, I would believe it foolish to not use them. However, they do come with additional costs to obtain/maintain/operate. You (well your business) needs to make a cost vs. benefit assessment, and chose what's "right for you".
I've used unmanaged switches to add some ports, usually temporarily, but even sometimes permanently (as in the case I need just one or a few additional ports, and don't want to purchase another all-up Enterprise grade switch). Having done such myself, and I have not, yet, have had a problem.
(BTW, when I've done it, for a few extra ports, I often find out, what's going to use these ports, and might "re-patch" so that user facing ports are on the Enterprise switch, but perhaps "move" a network printer to be on the unmanaged switch port.)
To summarize all the above, doing somethings adds risk, and sometimes that risk's potential harm's possibility of happening can be reduced or mitigated if it happens, but you need to consider the trade-offs, i.e. what's important to you.
I would advise not making such decisions based on just, well I heard this story about something very bad happening (like the Titanic sinking) or I head this story about something very good happening (like in my country, the recent 2.04 billion dollar single ticket lottery winner).
