Under the vast majority of circumstances, no. I avoid them. But there could always be that one coin that I'd like to have but has always been out of reach and suddenly one appears at a reasonable price but it has "details" on it. Hm. It could happen.
I would buy and have bought problem coins in the following situations: When the coin is sufficiently rare and problem free examples are either unavailable or unobtainably expensive. When the coin is struck in a highly reactive metal such as iron or zinc, and minor problems are par for the course. For example if I ruled out minor problems for my WWI Hungarian iron types I wouldn't have any examples at all. When the problem is minor and the coin is otherwise attractive (not all problems are created equal), provided the price is fair. Sometimes TPGs will even net grade these or consider them market acceptable as with old cleanings that have retoned. When a significantly better example can be found with a minor problem over a lower grade example. For example my draped bust quarter type coin has minor damage to the reverse, but VG details otherwise, and a very pleasing obverse. I paid around what I would have for a problem free AG, and got what I consider to be a much more appealing type coin. When it's priced way too low to pass up. A steal is a steal. It is perfectly reasonable to accept minor problems in all of the above scenarios. As long as the price is fair, why not consider an attractive problem coin?
Except for a few moderns, all of my coins are certified (clean grade). It's possible that a couple of them may not grade when submitting them again. Coins with an old cleaning may have been "market acceptable" at the time they were graded, but could come back "cleaned" today. Who knows? So I wouldn't buy any coins with obvious problems, because it would make my collection less special. Let's not forget I need a single coin of a certain type for my 7070 registry set, so why bother looking at problem coins?
#1, #3 and #4 above, especially #1 and #3. Most collectors collect coins that are too common where it doesn't make any sense to buy a problem coin. For those of us who do not, sometimes that is all that is available or is likely to be available. There isn't the luxury of choosing from multiple specimens (usually in close proximity) with hair splitting differences. In a few of my series, I have either seen most of the coins only in low grades or never in almost 15 years.
I would have no problem buying problem coins if the price is right (or a bargain) and if it's something that's uncommon to rare. Sometimes you really need to have the gut feel and make the impulse purchase even when a problem coin appears. There is a problem coin that I purchased a while back which went 10 times well over what Krause reckoned the value is. More than 5 years down the road, I've never seen another example. Should another example appear, I believe it would cause some sparking furious bids.
It depends on the problem. One of my collecting interests is the coinage of the colonial and early federal period in US History when foreign coins circulated as legal tender. Many of these coins came from regions where coins were frequently holed as a way of carrying them (strung on string about the neck) so for me a holed Spanish Piece of Eight Reales or a Portuguese half joe is indicative of actual use from that time. Gold from that period can be pretty pricey, so, for me, the only way I can afford that British guinea or French Louis d'or is if it is holed, or perhaps rim damaged from being looped or mounted. Half a loaf is fine when you are hungry.
This is an excellent point and something I wasn't even considering. It depends heavily on what you collect. Really anything where problem free examples are plentiful makes problem coins extremely undesirable. Take moderns for example. But for some sets, it's tough finding any example of a particular coin, problem or not. If your collection contains coins like that, of course you will be happy with problem coins. It's really an apples to oranges comparison. For example, my Washington quarters set doesn't have any problem coins and doesn't need to. They are plentiful in problem-free uncirculated grades. My capped bust quarters die marriage set has some problem coins. I have no problem paying the right price for a problem coin for that set if it's for an R4 or scarcer variety in the right die state. In my Habsburg coronation jetons/medals and Austro-Hungarian type set, some of the rarer issues I would be happy to find an example with a minor problem.
I've bought a few AU "details" coins... cheap & silver & old & U.S. But I draw the line at holes or similar damage. Never buy 'em.
For me it is a question of value when it comes to coins. As with any collector, I want to buy coins at prices that I believe are below market. This is why I voted that would only buy a problem coin (on purpose) if it were really cheap. This implies that there is a market for the coin, I got it for a good price, and I may sell it if and when I wanted to sell it.
I LOVE problem coins .... counterstamped, that is, akin to my avatar. These problem coins can literally tell you where they've been, who held them and what purpose they served. Ahh, the history! These are attributes that, provenance aside, the entombed, pristine coins can rarely offer. My hat's off to all the naysayers on "problem" coins ... More then will come my way!
I think the only "problem" coin I ever knowingly bought was a large cent that was in a details holder because of a scratch. I really didn't even notice the scratch and it was cheap. So, this boils down to 1) not an unattractive problem and 2) cheap.
Virtually never, I don't like being the bag-holder. However, my LCS submits a lot of coins and quite a few come back bagged. The owner usually asks my opinion on any Lincolns that come back. For a good number of them I cannot understand the TPG thinking! I have bought a couple of these from him since I thought the TPG was dead wrong, they were nice coins....and I got them cheaper than normal.
Not singling your coin out but I would not rely on Krause prices. The evidence proves they are mostly just made up and have no resemblance to reality.
It would have to depend on what it was. Nothing that's readily available would need to be purchased with a problem obviously. But it does put some pieces within reach that otherwise wouldn't be. As an example, the 1839-O $2.5 is a very popular first year of issue (mint mark on the front) that is often found in details slabs, for thousands of dollars. I've seen several I wouldn't mind having with a details grade. Despite the minor problem, the condition some can be obtained in would be multiples of the price without the problem, for the same example. Not that there's ever that many for sale anyway.
The demand for many US coins with "problems" is a lot more robust versus most coins from elsewhere. As an example, if I collected them, I might not mind buying early federal coinage (up to maybe 1807 or so) in a "details" or "genuine" holder to acquire an example that is actually better than a lower or much lower grade coin in a numerical holder. Maybe a coin with hairlines from a prior cleaning but with decent color and no other visible problems. Usually, I would prefer it to one which is (nearly) untoned. As other posts have stated here, there frequently isn't anything really wrong with these coins, regardless that they have not been deemed "market acceptable".