First, we commend you for doing the mitzva of hashavat aveida[1] so diligently. It is possible that some of the returning was unnecessary (for reasons beyond our scope), but one of the major Talmudic sources about the appropriateness of acting beyond the letter of the law discusses specifically the mitzva of hashavat aveida.[2]
The letter of the law in this area is quite demanding, applying even to an object worth a peruta (a few cents) and not clearly limiting the amount of toil one needs to expend.[3] You may demand compensation for related expenses and lost revenues,[4] but we doubt that you feel comfortable doing so. However, the essence of the mitzva is to help others, and at times the amount of effort is disproportionate to the recipient’s benefit, to the extent that it is likely that he would not have wanted you to bother. It seems that in cases in which this is likely but not clear enough to rely upon, the spirit of the law is that you should not have to bother, although the mitzva technically still applies. We bring up the spirit of the law, which cannot allow one to compromise the letter of the law, because when the spirit does not apply, it is acceptable to use a valid halachic device to exempt oneself from the mitzva, as we will discuss.
Often, shuls are inundated with unclaimed objects left behind, many of which will never successfully be returned to their owners.[5] Many institutions deal with the problem by posting signs stating that items that remain unclaimed for x days will be deemed hefker,[6] and in fact, several prominent poskim have advised using this method.[7] We propose that you use the same concept with some twists. In your case, in which it is relatively easy to track down some owners, it seems wrong to make the matter a function of time alone. Rather, we suggest writing in a lease or stating clearly to the renters before they occupy the apartment the following: “Anything that is worth less than $20 and apparently has no sentimental value will be held for two weeks. The renter exempts the landlord from making efforts to report finding such items and/or returning them, and the renter hereby relinquishes ownership of them as of two weeks after the end of the rental.” For more valuable or important items, you should continue extending yourself, when necessary, to fulfill the mitzva properly.
Let us briefly explain the mechanism of this provision. The gemara[8] discusses the action taken by a person who did not want the poor to unknowingly be obligated in tithes if they took more produce than the laws of matnot ani’im[9] allowed. He therefore declared in the morning that whatever extra produce the poor would take was hefker retroactively to the moment of the declaration.[10] The complication is that it is not clear which part of what they took was extra, and thus slated for hefker. Therefore, bereira (retroactive determination) is needed for the hefker to take effect, and the efficacy of the declaration consequently depends on the machloket among Tannaim regarding whether bereira works.[11] We rule that bereira does not work in regard to Torah laws.[12] How, then, can one be mafkir[13] an undetermined object that will be lost to exempt the finder from the Torah law of hashavat aveida? The answer is that bereira applies only when the determination must take effect retroactively.[14] If, however, the hefker can take effect later on, at the time the matter is determined (i.e., after x days, we know which items remain unclaimed), it works.[15]
Our formula above also includes an exemption from hashavat aveida prior to the hefker so that you should not be required to make efforts to return apparently unimportant items during the two weeks. This is based on the rule that the intended recipient of a mitzva between man and man can exempt another from performing the mitzva on his behalf.[16]