I'm trying to identify a book I read back in the late 1970s or early 1980s. It was a paperback science fiction anthology . . . The book's cover might have an illustration of a frog-like alien with tentacles, but I'm not sure about that detail.
This Side of Infinity, a 1972 paperback anthology edited by Terry Carr.
. . . and all I distinctly remember is two of the stories in it. One was a police story in which two officers rescue parents being held for ransom by their own young children, who have barricaded themselves in their home using high-tech toys as weapons.
"Toys", a short story by Tom Purdom:
"I had the computer call everybody in a twenty-house radius," the dispatcher said. "The reports are coming in now. Ten to twelve children have taken the Rice family hostage. They seem to be led by the Rice's nine year old son, Tim. Their main weapons seem to be their pets, but they may have other weapons inside the house. They want a committee of three parents to enter the house and negotiate with them, but they won't say what they want."
The "pets" are not dogs and cats, they are modified gorillas, elephants, tigers, and dragons. (Well, the "dragons" are modified lizards.) The high-tech toys include a "gravity changer".
The second was about an alien spy
"The Reality Trip", a short story by Robert Silverberg, first published in If, May–June 1970, available at the Internet Archive:
My daily routine rarely varies. I rise at seven. First Feeding. Then I clean my outer skin (my outer one, the Earthskin, I mean) and dress. From eight to ten I transmit data to Homeworld. Then I go out for the morning field trip: talking to people, buying newspapers, often some library research. At one I return to my room. Second Feeding. I transmit data from two to five. Out again, perhaps to the theater, to a motion picture, to a political meeting. I must soak up the flavor of this planet. Often to saloons—I am equipped for ingesting alcohol, though of course I must get rid of it before it has been in my body very long—and I drink and listen and sometimes argue. At midnight back to my room. Third Feeding. Transmit data from one to four in the morning. Then three hours of sleep and at seven the cycle begins anew. It is a comforting schedule. I don't know how many agents Homeworld has on Earth but I like to think I'm one of the most diligent and useful. I miss very little.
who lives in disguise inside a mechanical human body,
And the outer body I must wear. This cunning disguise. Forever to be swaddled in thick masses of synthetic flesh, smothering me, engulfing me. The soft slippery slap of it against the self within. The elaborate framework that holds it erect, by which I make it move—a forest of struts and braces and servoactuators and cables, in the midst of which I must unendingly huddle, atop my little platform in the gut.
and who is pursued romantically by his female neighbor.
I am a redemption project for her. She lives on my floor of the hotel, a dozen rooms down the hall: a lady poet, private income. No, that makes her sound too old, a middle-aged eccentric. Actually she is no more than thirty. Taller than I am, with long kinky brown hair and a sharp, bony nose that has a bump on the bridge. Eyes are very glossy. A studied raggedness about her dress—carefully chosen shabby clothes. I am in no position really to judge the sexual attractiveness of Earthfolk but I gather from remarks made by men living here that she is not considered good-looking. I pass her often on my way to my room. She smiles fiercely at me. Saying to herself, no doubt, You poor lonely man. Let me help you bear the burden of your unhappy life. Let me show you the meaning of love, for I, too, know what it is like to be alone. . . .
Initially rebuffing her advances, he even reveals his true appearance to her, but she still insists she loves him,
This is unreal and dreamlike to me. I have revealed myself, thinking to drive her away in terror; she is no longer aghast, and smiles at my strangeness. She kneels to get a better look. I move back a short way. Eyestalks fluttering—I am uneasy. I have somehow lost the upper hand in this encounter.
She says, "I knew you were unusual, but not like this. but it's all right. I can cope. I mean, the essential personality, that's what I fell in love with. Who cares that you're a crab-man from the Green Galaxy? Who cares that we can't ever be real lovers? I can make that sacrifice. It's your soul I dig, David. Go on. Close yourself up again. You don't look comfortable this way." The triumph of love. She will not abandon me, even now. Disaster. I crawl back into Knecht and lift his arms to his chest to seal it. Shock is glazing my consciousness: the enormity, the audacity. What have I done? Elizabeth watches, awed, even delighted. "Listen," she tells me, "you can trust me. I mean, if you're some kind of spy, checking out the Earth, I don't care. I don't care. I won't tell anybody. Don't you see? This is the biggest thing that ever happened to me. A chance to show that love isn't just physical, isn't just chemistry, that it's a soul trip, that it crosses not just racial lines but the lines of the whole damned species, the planet itself—"
and he eventually falls in love with her as well and severs contact with his home world.
Let me admit the truth: I love her.
January 1. The new year begins. I have sent my resignation to Homeworld and have destroyed my ultrawave equipment. The links are broken. Tomorrow, when the city offices are open, Elizabeth and I will go to get the marriage license.